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Journal articles on the topic 'Quantum field theory; Curved spacetime'

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Published: 4 June 2021

Last updated: 8 February 2022

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1

Freitas, Gabriel, and Marc Casals. "A novel method for renormalization in quantum-field theory in curved spacetime." International Journal of Modern Physics D 27, no. 11 (August 2018): 1843001. http://dx.doi.org/10.1142/s0218271818430010.

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In quantum-field theory in curved spacetime, two important physical quantities are the expectation value of the stress-energy tensor [Formula: see text] and of the square of the field operator [Formula: see text]. These expectation values must be renormalized, which is usually performed via the so-called point-splitting prescription. However, the renormalization method that is usually implemented in the literature, in principle, only applies to static, spherically-symmetric spacetimes, and does not readily generalize to other types of spacetime. We present a novel implementation of the renormalization procedure which may be used in the future for more general spacetimes, such as Kerr black hole spacetime. As an example, we apply our method to the renormalization of [Formula: see text] for a massless scalar field in Bertotti–Robinson spacetime.

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2

GUIDO, D., R. LONGO, J. E. ROBERTS, and R. VERCH. "CHARGED SECTORS, SPIN AND STATISTICS IN QUANTUM FIELD THEORY ON CURVED SPACETIMES." Reviews in Mathematical Physics 13, no. 02 (February 2001): 125–98. http://dx.doi.org/10.1142/s0129055x01000557.

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The first part of this paper extends the Doplicher–Haag–Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group can be constructed as in Minkowski spacetime. The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with "modular covariance" for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild–Kruskal black holes, "geometric modular action" of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3).

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3

KAY, BERNARD S. "THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES." Reviews in Mathematical Physics 04, spec01 (December 1992): 167–95. http://dx.doi.org/10.1142/s0129055x92000194.

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In the context of a linear model (the covariant Klein Gordon equation) we review the mathematical and conceptual framework of quantum field theory on globally hyperbolic spacetimes, and address the question of what it might mean to quantize a field on a non globally hyperbolic spacetime. Our discussion centres on the notion of F-locality which we introduce and which asserts there is a net of local algebras such that every neighbourhood of every point contains a globally hyperbolic subneighbourhood of that point for which the field algebra coincides with the algebra one would obtain were one to regard the subneighbourhood as a spacetime in its own right and quantize — with some choice of time-orientation — according to the standard rules for quantum field theory on globally hyperbolic spacetimes. We show that F-locality is a property of the standard field algebra construction for globally hyperbolic spacetimes, and argue that it (or something similar) should be imposed as a condition on any field algebra construction for non globally hyperbolic spacetimes. We call a spacetime for which there exists a field algebra satisfying F-locality F-quantum compatible and argue that a spacetime which did not satisfy something similar to this condition could not arise as an approximate classical description of a state of quantum gravity and would hence be ruled out physically. We show that all F-quantum compatible spacetimes are time orientable. We also raise the issue of whether chronology violating spacetimes can be F-quantum compatible, giving a special model — a massless field theory on the “four dimensional spacelike cylinder” — which is F-quantum compatible, and a (two dimensional) model — a massless field theory on Misner space — which is not. We discuss the possible relevance of this latter result to Hawking’s recent Chronology Protection Conjecture.

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4

KRÓL, JERZY. "TOPOS THEORY AND SPACETIME STRUCTURE." International Journal of Geometric Methods in Modern Physics 04, no. 02 (March 2007): 297–303. http://dx.doi.org/10.1142/s0219887807002028.

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According to the recently proposed model of spacetime, various difficulties of quantum field theories and semiclassical quantum gravity on curved 4-Minkowski spacetimes gain new formulations, leading to new solutions. The quantum mechanical effects appear naturally when diffeomorphisms are lifted to 2-morphisms between topoi. The functional measures can be well defined. Diffeomorphisms invariance and background independence are approached from the perspective of topoi. In the spacetimes modified at short distances by the internal structure of some topoi, the higher dimensional regions appear and field/strings duality emerges. We show that the model has natural extensions over extremely strong gravity sources in spacetime and shed light on the strong string coupling definition of B-type D-branes.

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5

de Medeiros, Paul, and Stefan Hollands. "Superconformal quantum field theory in curved spacetime." Classical and Quantum Gravity 30, no. 17 (August 21, 2013): 175015. http://dx.doi.org/10.1088/0264-9381/30/17/175015.

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6

Hollands, Stefan, and Robert M. Wald. "Axiomatic Quantum Field Theory in Curved Spacetime." Communications in Mathematical Physics 293, no. 1 (September 1, 2009): 85–125. http://dx.doi.org/10.1007/s00220-009-0880-7.

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7

Bernar, Rafael P., Luís C. B. Crispino, and Atsushi Higuchi. "Circular geodesic radiation in Schwarzschild spacetime: A semiclassical approach." International Journal of Modern Physics D 27, no. 11 (August 2018): 1843002. http://dx.doi.org/10.1142/s0218271818430022.

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Extreme curvature settings and nontrivial causal structure of curved spacetimes may have interesting theoretical and practical implications for quantum field theories. Radiation emission in black hole spacetimes is one such scenario in which the semiclassical approach, i.e. quantum fields propagating in a nondynamical background spacetime, adds a very simple conceptual point of view and allows us to compute the emitted power in a straightforward way. Within this context, we reexamine sources in circular orbit around a Schwarzschild black hole, investigating the emission of scalar, electromagnetic and gravitational radiations. The analysis of the differences and similarities between these cases provide an excellent overview of the powerful conceptual and computational tool that is quantum field theory in curved spacetime.

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8

Sorkin, Rafael D. "From Green function to quantum field." International Journal of Geometric Methods in Modern Physics 14, no. 08 (May 11, 2017): 1740007. http://dx.doi.org/10.1142/s0219887817400072.

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A pedagogical introduction to the theory of a Gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function [Formula: see text] regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at [Formula: see text] starting from nothing but the retarded Green function [Formula: see text]. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished “vacuum” or “ground state”, and to recognize some interesting formal relationships, including a general condition on [Formula: see text] expressing zero-entropy or “purity”.

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9

Diel, Hans H. "A Model of Spacetime Dynamics with Embedded Quantum Objects." Reports in Advances of Physical Sciences 01, no. 03 (September 2017): 1750010. http://dx.doi.org/10.1142/s2424942417500104.

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General relativity theory (GRT) tells us that (a) space and time should be viewed as an entity (called spacetime), (b) the spacetime of a world that contains gravitational objects should be viewed as curved, and (c) spacetime is a dynamical object with a dynamically changing extent and curvature. Attempts to achieve compatibility of GRT with quantum theory (QT) have typically resulted in proposing elementary units of spacetime as building blocks for the emergence of larger spacetime objects. In the present paper, a model of curved discrete spacetime is presented in which the basic space elements are derived from Causal Dynamical Triangulation. Spacetime can be viewed as the container for physical objects, and in GRT, the energy distribution of the contained physical objects determines the dynamics of spacetime. In the proposed model of curved discrete spacetime, the primary objects contained in spacetime are “quantum objects”. Other larger objects are collections of quantum objects. This approach results in an accordance of GRT and quantum (field) theory, while coincidently the areas in which their laws are in force are separated. In the second part of the paper, a rough mapping of quantum field theory to the proposed model of spacetime dynamics is described.

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10

Toms, D. J. "Functional measure for quantum field theory in curved spacetime." Physical Review D 35, no. 12 (June 15, 1987): 3796–803. http://dx.doi.org/10.1103/physrevd.35.3796.

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11

HOLLANDS, STEFAN. "RENORMALIZED QUANTUM YANG–MILLS FIELDS IN CURVED SPACETIME." Reviews in Mathematical Physics 20, no. 09 (October 2008): 1033–172. http://dx.doi.org/10.1142/s0129055x08003420.

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We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang–Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensures conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators. The key technical tool behind these arguments is a new universal Ward identity that is formulated at the algebraic level, and that is proven to be consistent with a local and covariant renormalization prescription. We also develop a new technique to accomplish this renormalization process, and in particular give a new expression for some of the renormalization constants in terms of cycles.

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12

Sanchez, N. G. "Advances in String Theory in Curved Backgrounds: A Synthesis Report." International Journal of Modern Physics A 18, no. 12 (May 10, 2003): 2011–22. http://dx.doi.org/10.1142/s0217751x0301543x.

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A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely : the new feature of Multistring solutions; the mass spectrum of Strings in Curved backgrounds; The effect of a Cosmological Constant and of Spacial Curvature on Classical and Quantum Strings; Classical splitting of Fundamental Strings; The General String Evolution in constant Curvature Spacetimes; The Conformal Invariance Effects; Strings on plane fronted and gravitational shock waves, string falling on spacetime singularities and its spectrum. New Developments in String Gravity and String Cosmology are reported: String driven cosmology and its Predictions; The primordial gravitational wave background; Non-singular string cosmologies from Exact Conformal Field Theories; Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time; Hawking Radiation in String Theory and the String Phase of Black Holes; New Dual Relation between Quantum Field Theory regime and String regime and the "QFT/String Tango"; New Coherent String States and Minimal Uncertainty Principle in string theory.

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13

Avetisyan, Zhirayr, and Matteo Capoferri. "Partial Differential Equations and Quantum States in Curved Spacetimes." Mathematics 9, no. 16 (August 13, 2021): 1936. http://dx.doi.org/10.3390/math9161936.

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In this review paper, we discuss the relation between recent advances in the theory of partial differential equations and their applications to quantum field theory on curved spacetimes. In particular, we focus on hyperbolic propagators and the role they play in the construction of physically admissible quantum states—the so-called Hadamard states—on globally hyperbolic spacetimes. We will review the notion of a propagator and discuss how it can be constructed in an explicit and invariant fashion, first on a Riemannian manifold and then on a Lorentzian spacetime. Finally, we will recall the notion of Hadamard state and relate the latter to hyperbolic propagators via the wavefront set, a subset of the cotangent bundle capturing the information about the singularities of a distribution.

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14

Colosi, Daniele. "On Unitary Evolution in Quantum Field Theory in Curved Spacetime." Open Nuclear & Particle Physics Journal 4, no. 1 (August 19, 2011): 13–20. http://dx.doi.org/10.2174/1874415x01104010013.

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15

HOLLANDS, STEFAN, and ROBERT M. WALD. "CONSERVATION OF THE STRESS TENSOR IN PERTURBATIVE INTERACTING QUANTUM FIELD THEORY IN CURVED SPACETIMES." Reviews in Mathematical Physics 17, no. 03 (April 2005): 227–311. http://dx.doi.org/10.1142/s0129055x05002340.

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We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple "Principle of Perturbative Agreement": for interaction Lagrangians L1 that are such that the interacting field theory can be constructed exactly — as occurs when L1 is a "pure divergence" or when L1 is at most quadratic in the field and contains no more than two derivatives — then time-ordered products must be defined so that the perturbative solution for interacting fields obtained from the Bogoliubov formula agrees with the exact solution. The conditions derived from this principle include a version of the Leibniz rule (or "action Ward identity") and a condition on time-ordered products that contain a factor of the free field φ or the free stress-energy tensor Tab. The main results of our paper are (1) a proof that in spacetime dimensions greater than 2, our new conditions can be consistently imposed in addition to our previously considered conditions and (2) a proof that, if they are imposed, then for any polynomial interaction Lagrangian L1 (with no restriction on the number of derivatives appearing in L1), the stress-energy tensor Θab of the interacting theory will be conserved. Our work thereby establishes (in the context of perturbation theory) the conservation of stress-energy for an arbitrary interacting scalar field in curved spacetimes of dimension greater than 2. Our approach requires us to view time-ordered products as maps taking classical field expressions into the quantum field algebra rather than as maps taking Wick polynomials of the quantum field into the quantum field algebra.

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16

Mandal, Susobhan. "Classification of quantum states based on the null energy condition." Modern Physics Letters A 36, no. 25 (August 20, 2021): 2150183. http://dx.doi.org/10.1142/s0217732321501832.

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Violation of the null energy condition plays an important role both in the general theory of relativity and quantum field theory in curved spacetimes. Over the years, it has been shown that the violation of the null energy condition leads to instability and violation of causality. In quantum field theory, violation of the energy condition also depends on the quantum states apart from the geometry of curved spacetime. Hence, the quantum effects play an important role in the violation of the null energy condition. We show that the set of all the coherent states does not violate the null energy condition. Further, we also show that under certain conditions, the null energy condition is violated either by a pure state or a mixed state. Furthermore, the dynamical violation of the null energy condition by the quantum states is also discussed here.

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17

Hu, B. L., R. Critchley, and Aris Stylianopoulos. "Finite-temperature quantum field theory in curved spacetime: Quasilocal effective Lagrangians." Physical Review D 35, no. 2 (January 15, 1987): 510–27. http://dx.doi.org/10.1103/physrevd.35.510.

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18

Maybee, Ben, Daniel Hodgson, Almut Beige, and Robert Purdy. "A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes." Entropy 21, no. 9 (August 30, 2019): 844. http://dx.doi.org/10.3390/e21090844.

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Recently, Bennett et al. (Eur. J. Phys. 37:014001, 2016) presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, H ^ , and the electric and magnetic field observables, E ^ and B ^ , respectively, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect.

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19

Castro, Carlos. "A gauge theory of gravity in curved phase-spaces." International Journal of Geometric Methods in Modern Physics 13, no. 07 (July 25, 2016): 1650097. http://dx.doi.org/10.1142/s0219887816500973.

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After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann–Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the [Formula: see text] cotangent bundle [Formula: see text] of spacetime is explicitly constructed and based on the gauge group [Formula: see text] which acts on the tangent space to the cotangent bundle [Formula: see text] at each point [Formula: see text]. Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.

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20

Agulló, Iván, Adrián del Río, and José Navarro-Salas. "On the Electric-Magnetic Duality Symmetry: Quantum Anomaly, Optical Helicity, and Particle Creation." Symmetry 10, no. 12 (December 17, 2018): 763. http://dx.doi.org/10.3390/sym10120763.

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It is well known that not every symmetry of a classical field theory is also a symmetry of its quantum version. When this occurs, we speak of quantum anomalies. The existence of anomalies imply that some classical Noether charges are no longer conserved in the quantum theory. In this paper, we discuss a new example for quantum electromagnetic fields propagating in the presence of gravity. We argue that the symmetry under electric-magnetic duality rotations of the source-free Maxwell action is anomalous in curved spacetimes. The classical Noether charge associated with these transformations accounts for the net circular polarization or the optical helicity of the electromagnetic field. Therefore, our results describe the way the spacetime curvature changes the helicity of photons and opens the possibility of extracting information from strong gravitational fields through the observation of the polarization of photons. We also argue that the physical consequences of this anomaly can be understood in terms of the asymmetric quantum creation of photons by the gravitational field.

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21

Guillen Gomez, Alfonso Leon. "Is Gravity, The Curvature of Spacetime or A Quantum Phenomenon?" JOURNAL OF ADVANCES IN PHYSICS 4, no. 1 (March 22, 2014): 449–59. http://dx.doi.org/10.24297/jap.v4i1.2046.

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Gravity is the curvature of spacetime, the structural property of static gravitational field, a geometric field, in curved coordinates, according the functions guv, that express geometric relations. Course, general relativity is a relational theory, however, gravity, a thinking category, has symetric physical effects with matter. Throught of relativist aether was attempted transform spacetime in a substantia without succes, the consequence was return to problematic geometric field. The philosophy of the science intervenes, and according the substantialist theory spacetime is a inmaterial, geometric substantia. Then, the metaphysics arrives to a full solution in the super-substantivalist theory, that affirms: matter arises from geometric spacetime. Thus, it explains consistently the symetric physical effects between spacetime and matter. Surely, this solution is a medieval speculation. Our goal is driver the debate on gravity, to the arena of the quantum physics, but without the ballast of the general relativity. Â Â

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22

DE BERREDO-PEIXOTO, G. "ON THE 1-LOOP CALCULATIONS OF SOFTLY BROKEN FERMION-TORSION THEORY IN CURVED SPACE USING THE STÜCKELBERG PROCEDURE." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1570–73. http://dx.doi.org/10.1142/s0217751x09045017.

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The soft breaking of gauge or other symmetries is the typical Quantum Field Theory phenomenon. In many cases one can apply the Stückelberg procedure, which means introducing some additional field (or fields) and restore the gauge symmetry. The original softly broken theory corresponds to a particular choice of the gauge fixing condition. In this paper we use this scheme for performing quantum calculations for fermion-torsion theory, softly broken by the torsion mass in arbitrary curved spacetime.

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23

Summers, Stephen J., and Rainer Verch. "Modular inclusion, the Hawking temperature, and quantum field theory in curved spacetime." Letters in Mathematical Physics 37, no. 2 (June 1996): 145–58. http://dx.doi.org/10.1007/bf00416017.

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24

Hollands, Stefan. "The Operator Product Expansion for Perturbative Quantum Field Theory in Curved Spacetime." Communications in Mathematical Physics 273, no. 1 (April 28, 2007): 1–36. http://dx.doi.org/10.1007/s00220-007-0230-6.

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25

Alekseev, D. V., and I. L. Shapiro. "Group-renormalization approach in quantum field theory in curved spacetime with torsion." Soviet Physics Journal 33, no. 10 (October 1990): 840–43. http://dx.doi.org/10.1007/bf00897305.

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26

Odintsov, S. D. "Vilkovisky-de Witt effective action in quantum field theory in curved spacetime." Soviet Physics Journal 34, no. 4 (April 1991): 370–73. http://dx.doi.org/10.1007/bf00898106.

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27

Fewster, Christopher J., and Rainer Verch. "Quantum Fields and Local Measurements." Communications in Mathematical Physics 378, no. 2 (July 27, 2020): 851–89. http://dx.doi.org/10.1007/s00220-020-03800-6.

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Abstract The process of quantum measurement is considered in the algebraic framework of quantum field theory on curved spacetimes. Measurements are carried out on one quantum field theory, the “system”, using another, the “probe”. The measurement process involves a dynamical coupling of “system” and “probe” within a bounded spacetime region. The resulting “coupled theory” determines a scattering map on the uncoupled combination of the “system” and “probe” by reference to natural “in” and “out” spacetime regions. No specific interaction is assumed and all constructions are local and covariant. Given any initial state of the probe in the “in” region, the scattering map determines a completely positive map from “probe” observables in the “out” region to “induced system observables”, thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. Post-selected states conditioned on measurement outcomes are obtained using Davies–Lewis instruments that depend on the initial probe state. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument; in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework. The general concepts and results are illustrated by an example in which both “system” and “probe” are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory.

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SAHLMANN, HANNO, and RAINER VERCH. "MICROLOCAL SPECTRUM CONDITION AND HADAMARD FORM FOR VECTOR-VALUED QUANTUM FIELDS IN CURVED SPACETIME." Reviews in Mathematical Physics 13, no. 10 (October 2001): 1203–46. http://dx.doi.org/10.1142/s0129055x01001010.

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Some years ago, Radzikowski has found a characterization of Hadamard states for scalar quantum fields on a four-dimensional globally hyperbolic spacetime in terms of a specific form of the wavefront set of their two-point functions (termed "wavefront set spectrum condition"), thereby initiating a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, we extend this important result on the equivalence of the wavefront set spectrum condition with the Hadamard condition from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance saling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.

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JUNKER, WOLFGANG. "HADAMARD STATES, ADIABATIC VACUA AND THE CONSTRUCTION OF PHYSICAL STATES FOR SCALAR QUANTUM FIELDS ON CURVED SPACETIME." Reviews in Mathematical Physics 08, no. 08 (November 1996): 1091–159. http://dx.doi.org/10.1142/s0129055x9600041x.

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Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. After a short mathematical review techniques from the theory of pseudodifferential operators and wavefront sets on manifolds are used to develop a criterion for a state to be an Hadamard state. It is proven that ground- and KMS-states on certain static spacetimes and adiabatic vacuum states on Robertson-Walker spaces are Hadamard states. A counterexample is given which shows that the idea of instantaneous positive energy states w.r.t. a Cauchy surface does in general not yield physical states. Finally, the problem of constructing Hadamard states on arbitrary curved spacetimes is solved in principle.

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Costa, H. A. S., and P. R. S. Carvalho. "NLO critical exponents of O(N) λ ϕ4 scalar field theories in curved spacetime." International Journal of Modern Physics D 28, no. 01 (January 2019): 1950024. http://dx.doi.org/10.1142/s021827181950024x.

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In this paper, we investigate analytically the conformal symmetry influence on the next-to-leading order radiative quantum corrections to critical exponents for massless O([Formula: see text]) [Formula: see text] scalar field theories in curved spacetime. We renormalize the theory by applying the Bogoliubov–Parasyuk–Hepp–Zimmermann (BPHZ) method. We find that the critical exponents are the same as that of flat spacetime, at least at the loop order considered. We argue that this result agrees perfectly with the universality hypothesis.

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ARZANO, MICHELE. "QUANTUM FIELDS ON CURVED MOMENTUM SPACE." International Journal of Geometric Methods in Modern Physics 09, no. 06 (August 3, 2012): 1261002. http://dx.doi.org/10.1142/s0219887812610026.

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Relativistic particles with momentum space described by a group manifold provide a very interesting link between gravity, quantum group symmetries and non-commutative field theories. We discuss how group valued momenta emerge in the context of three-dimensional Einstein gravity and describe the related non-commutative field theory. As an application we introduce a non-commutative heat-kernel, calculate the associated spectral dimension and comment on its non-trivial behavior. In four spacetime dimensions the only known example of momenta living on a group manifold is encountered in the context of the κ-Poincaré algebra introduced by Lukierski et al. 20 years ago. I will discuss the construction of a one-particle Hilbert space from the classical κ-deformed phase space and show how the group manifold structure of momentum space leads to an ambiguity in the quantization procedure. The tools introduced in the discussion of field quantization lead to a natural definition of deformed two-point function.

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Fewster, Christopher J. "The art of the state." International Journal of Modern Physics D 27, no. 11 (August 2018): 1843007. http://dx.doi.org/10.1142/s0218271818430071.

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Quantum field theory (QFT) on curved spacetimes lacks an obvious distinguished vacuum state. We review a recent no-go theorem that establishes the impossibility of finding a preferred state in each globally hyperbolic spacetime, subject to certain natural conditions. The result applies in particular to the free scalar field, but the proof is model-independent and therefore of wider applicability. In addition, we critically examine the recently proposed “SJ states”, that are determined by the spacetime geometry alone, but which fail to be Hadamard in general. We describe a modified construction that can yield an infinite family of Hadamard states, and also explain recent results that motivate the Hadamard condition without direct reference to ultra-high energies or ultra-short distance structure.

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33

Hollands, Stefan, and Robert M. Wald. "Quantum field theory in curved spacetime, the operator product expansion, and dark energy." General Relativity and Gravitation 40, no. 10 (August 1, 2008): 2051–59. http://dx.doi.org/10.1007/s10714-008-0672-y.

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34

Lewis, Adam G. M., and Guifré Vidal. "Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme." Quantum 4 (October 28, 2020): 351. http://dx.doi.org/10.22331/q-2020-10-28-351.

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We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime and how to compute renormalized expectation values in the Hawking-Hartle vacuum of a Schwarzschild black hole and in the Bunch-Davies vacuum of an expanding universe described by de Sitter spacetime. Although here we address a non-interacting QFT using free fermion techniques, the framework described in this paper lays the groundwork for a series of subsequent studies involving simulation of interacting QFTs in curved spacetime by tensor network techniques.

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35

VERCH, RAINER, and REINHARD F. WERNER. "DISTILLABILITY AND POSITIVITY OF PARTIAL TRANSPOSES IN GENERAL QUANTUM FIELD SYSTEMS." Reviews in Mathematical Physics 17, no. 05 (June 2005): 545–76. http://dx.doi.org/10.1142/s0129055x05002364.

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Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of degrees-of-freedom, including quantum fields. We show that a large number of states in relativistic quantum field theory, including the vacuum state and thermal equilibrium states, are distillable over subsystems separated by arbitrary spacelike distances. These results apply to any quantum field model. It will also be shown that these results can be generalized to quantum fields in curved spacetime, leading to the conclusion that there is a large number of quantum field states which are distillable over subsystems separated by an event horizon.

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36

Fewster, Christopher J. "Locally covariant quantum field theory and the spin–statistics connection." International Journal of Modern Physics D 25, no. 06 (May 2016): 1630015. http://dx.doi.org/10.1142/s0218271816300159.

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The framework of locally covariant quantum field theory (QFT), an axiomatic approach to QFT in curved spacetime (CST), is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which allows for a more operational description of theories with spin and for the derivation of a more general version of the spin–statistics connection in CSTs than previously available. This part of the text is based on [C. J. Fewster, arXiv:1503.05797.] and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation.

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BARCELÓ, CARLOS, and LUIS J. GARAY. "WORMHOLE EFFECTIVE INTERACTIONS IN ANTI-DE SITTER SPACETIME." International Journal of Modern Physics D 07, no. 04 (August 1998): 623–45. http://dx.doi.org/10.1142/s0218271898000425.

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The effects of asymptotically anti-de Sitter wormholes in low-energy field theory are calculated in full detail for three different matter contents: a conformal scalar field, an electromagnetic field and gravitons. There exists a close relation between the choice of vacuum for the matter fields and the selection of a basis of the Hilbert space of anti-de Sitter wormholes. In the presence of conformal matter (i.e., conformal scalar or electromagnetic fields), this relation allows us to interpret the elements of these bases as wormhole states containing a given number of particles. This interpretation is subject to the same kind of ambiguity in the definition of particle as that arising from quantum field theory in curved spacetime. In the case of gravitons, owing to the nonconformal coupling, it is not possible to describe wormhole states in terms of their particle content.

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Arrighi, Pablo, and Stefno Facchini. "Quantum walking in curved spacetime: (3+1) dimensions, and beyond." Quantum Information and Computation 17, no. 9&10 (August 2017): 810–24. http://dx.doi.org/10.26421/qic17.9-10-4.

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A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently it was discovered that prior grouping and encoding allows for more general continuum limit equations (e.g. the Dirac equation in (1+ 1) curved spacetime). In this paper, we extend these results to arbitrary space dimension and internal degree of freedom. We recover an entire class of PDEs encompassing the massive Dirac equation in (3 + 1) curved spacetime. This means that the metric field can be represented by a field of local unitaries over a lattice.

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39

Calzetta, E., S. Habib, and B. L. Hu. "Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations." Physical Review D 37, no. 10 (May 15, 1988): 2901–19. http://dx.doi.org/10.1103/physrevd.37.2901.

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40

Galstian, Anahit, and Karen Yagdjian. "Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime." Reviews in Mathematical Physics 32, no. 07 (December 20, 2019): 2050018. http://dx.doi.org/10.1142/s0129055x2050018x.

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We examine the solutions of the semilinear wave equation, and, in particular, of the [Formula: see text] model of quantum field theory in the curved spacetime. More exactly, for [Formula: see text] we prove that the solution of the massless self-interacting scalar field equation in the Einstein–de Sitter universe has finite lifespan.

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41

Lawrie, Ian D. "Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, by L. Parker and D. Toms." Contemporary Physics 52, no. 2 (March 2011): 158–59. http://dx.doi.org/10.1080/00107514.2010.534183.

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42

ODINTSOV, S., and R. PERCACCI. "YANG–MILLS VACUUM STRUCTURE AND QUANTUM GRAVITY." Modern Physics Letters A 11, no. 22 (July 20, 1996): 1807–14. http://dx.doi.org/10.1142/s021773239600179x.

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Using renormalization group methods, we calculate the derivative expansion of the effective Lagrangian for a covariantly constant gauge field in curved spacetime. Curvature affects the vacuum; in particular it could induce phase transitions between different vacua. We also consider the effect of quantum fluctuations of the metric, in the context of a renormalizable R2 theory. In this case the critical curvature depends on the gravitational coupling constants.

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Bilic, Neven, and Dijana Tolic. "Analogue cosmology in a hadronic fluid." Facta universitatis - series: Physics, Chemistry and Technology 12, no. 2 (2014): 77–83. http://dx.doi.org/10.2298/fupct1402077b.

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Analog gravity models of general relativity seem promising routes to providing laboratory tests of the foundation of quantum field theory in curved space-time. In contrast to general relativity, where geometry of a spacetime is determined by the Einstein equations, in analog models geometry and evolution of analog spacetime are determined by the equations of fluid mechanics. In this paper we study the analogue gravity model based on massless pions propagating in a expanding hadronic fluid. The analog expanding spacetime takes the form of an FRW universe, with the apparent and trapping horizons defined in the standard way.

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Fredenhagen, Klaus, and Kasia Rejzner. "Quantum field theory on curved spacetimes: Axiomatic framework and examples." Journal of Mathematical Physics 57, no. 3 (March 2016): 031101. http://dx.doi.org/10.1063/1.4939955.

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MAZZITELLI, FRANCISCO DIEGO. "QUANTUM FIELDS WITH MODIFIED DISPERSION RELATIONS IN CURVED SPACES." International Journal of Modern Physics D 20, no. 05 (May 20, 2011): 745–56. http://dx.doi.org/10.1142/s0218271811019086.

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We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

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TAKOOK, MOHAMMAD VAHID. "A NATURAL RENORMALIZATION OF THE ONE-LOOP EFFECTIVE ACTION FOR SCALAR FIELD IN CURVED SPACETIME." International Journal of Modern Physics E 14, no. 02 (March 2005): 219–23. http://dx.doi.org/10.1142/s0218301305002953.

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It has been shown that the negative norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter space.1,2 In this process, ultraviolet and infrared divergences have been automatically eliminated.3 A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λϕ4 theory) has been achieved through the consideration of the negative norm states.4 The one-loop effective action for scalar field in a general curved space-time has been calculated by this method, and a natural renormalization procedure in the one-loop approximation has been established.

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Iorio, Alfredo. "Curved spacetimes and curved graphene: A status report of the Weyl symmetry approach." International Journal of Modern Physics D 24, no. 05 (March 18, 2015): 1530013. http://dx.doi.org/10.1142/s021827181530013x.

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This is a status report about the ongoing work on the realization of quantum field theory on curved graphene spacetimes that uses Weyl symmetry. The programme is actively pursued from many different perspectives. Here we point to what has been done, and to what needs to be done.

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Hollands, S., and W. Ruan. "The State Space of Perturbative Quantum Field Theory in Curved Spacetimes." Annales Henri Poincaré 3, no. 4 (August 2002): 635–57. http://dx.doi.org/10.1007/s00023-002-8629-2.

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LIBERATI, STEFANO, TONY ROTHMAN, and SEBASTIANO SONEGO. "EXTREMAL BLACK HOLES AND THE LIMITS OF THE THIRD LAW." International Journal of Modern Physics D 10, no. 01 (February 2001): 33–39. http://dx.doi.org/10.1142/s0218271801000937.

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Recent results of quantum field theory on a curved spacetime suggest that extremal black holes are not thermal objects and that the notion of zero temperature is ill-defined for them. If this is correct, one may have to go to a full semiclassical theory of gravity, including backreaction, in order to make sense of the third law of black hole thermodynamics. Alternatively it is possible that we shall have to drastically revise the status of extremality in black hole thermodynamics.

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Yang, Shu-Zheng, Kai Lin, Jin Li, and Qing-Quan Jiang. "Lorentz Invariance Violation and Modified Hawking Fermions Tunneling Radiation." Advances in High Energy Physics 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7058764.

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Recently the modified Dirac equation with Lorentz invariance violation has been proposed, which would be helpful to resolve some issues in quantum gravity theory and high energy physics. In this paper, the modified Dirac equation has been generalized in curved spacetime, and then fermion tunneling of black holes is researched under this correctional Dirac field theory. We also use semiclassical approximation method to get correctional Hamilton-Jacobi equation, so that the correctional Hawking temperature and correctional black hole’s entropy are derived.

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