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Journal articles on the topic 'Quantum Field Theory in curved space-time'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Keller, Ole, and Lee M. Hively. "Electrodynamics in curved space-time: Free-space longitudinal wave propagation." Physics Essays 32, no. 3 (September 11, 2019): 282–91. http://dx.doi.org/10.4006/0836-1398-32.3.282.

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Jiménez and Maroto [Phys. Rev. D 83, 023514 (2011)] predicted free-space, longitudinal electrodynamic waves in curved space-time, if the Lorenz condition is relaxed. A general-relativistic extension of Woodside’s electrodynamics [Am. J. Phys. 77, 438 (2009)] includes a dynamical, scalar field in both the potential- and electric/magnetic-field formulations without mixing the two. We formulate a longitudinal-wave theory, eliminating curvature polarization, magnetization density, and scalar field in favor of the electric/magnetic fields and the metric tensor. We obtain a wave equation for the longitudinal electric field for a spatially flat, expanding universe with a scale factor. This work is important, because: (i) the scalar- and longitudinal-fields do not cancel, as in classical quantum electrodynamics; and (ii) this new approach provides a first-principles path to an extended quantum theory that includes acceleration and gravity.

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2

Folacci, A. "Quantum field theory ofp‐forms in curved space‐time." Journal of Mathematical Physics 32, no. 10 (October 1991): 2813–27. http://dx.doi.org/10.1063/1.529072.

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3

Audretsch, J�rgen. "Optical theorem in curved space-time quantum field theory." International Journal of Theoretical Physics 28, no. 9 (September 1989): 957–66. http://dx.doi.org/10.1007/bf00670341.

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4

KALINOWSKI, M. W., and W. PIECHOCKI. "GEOMETRIC QUANTIZATION OF FIELD THEORY ON CURVED SPACE–TIME." International Journal of Modern Physics A 14, no. 07 (March 20, 1999): 1087–110. http://dx.doi.org/10.1142/s0217751x99000543.

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A symplectic structure of classical field theory and its application to the canonical geometric quantization procedure are presented. The developed formalism can be treated in two ways: as a prequantization procedure in the usual sense or as a quantization procedure in a stochastic quantum mechanics approach on a phase space.

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5

Laciana, Carlos E. "Quantum field theory in curved space-time as thermo field dynamics." General Relativity and Gravitation 26, no. 4 (April 1994): 363–78. http://dx.doi.org/10.1007/bf02105227.

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6

BREVIK, IVER H., HERNÁN OCAMPO, and SERGEI ODINTSOV. "ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME." International Journal of Modern Physics A 13, no. 16 (June 30, 1998): 2857–74. http://dx.doi.org/10.1142/s0217751x98001451.

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We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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7

Ipek, Selman, Mohammad Abedi, and Ariel Caticha. "Entropic dynamics: reconstructing quantum field theory in curved space-time." Classical and Quantum Gravity 36, no. 20 (September 27, 2019): 205013. http://dx.doi.org/10.1088/1361-6382/ab436c.

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8

Gass, Richard, and Max Dresden. "Puzzling Aspect of Quantum Field Theory in Curved Space-Time." Physical Review Letters 54, no. 21 (May 27, 1985): 2281–84. http://dx.doi.org/10.1103/physrevlett.54.2281.

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9

Gass, Richard, and Max Dresden. "Puzzling Aspect of Quantum Field Theory in Curved Space-Time." Physical Review Letters 56, no. 12 (March 24, 1986): 1316. http://dx.doi.org/10.1103/physrevlett.56.1316.

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10

HOLLANDS, STEFAN, and ROBERT M. WALD. "QUANTUM FIELD THEORY IN CURVED SPACE–TIME, THE OPERATOR PRODUCT EXPANSION, AND DARK ENERGY." International Journal of Modern Physics D 17, no. 13n14 (December 2008): 2607–15. http://dx.doi.org/10.1142/s021827180801414x.

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To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved space–time, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved space–time does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a "vacuum state" and "particles". We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients — and, thus, the quantum field theory. By contrast, ground/vacuum states — in space–times, such as Minkowski space–time, where they may be defined — cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.

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11

Meister, A. "Complex manifold methods in quantum field theory in curved space‐time." Journal of Mathematical Physics 30, no. 12 (December 1989): 2930–42. http://dx.doi.org/10.1063/1.528480.

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12

Buchbinder, I. L., S. D. Odintsov, and I. L. Shapiro. "Renormalization group approach to quantum field theory in curved space-time." La Rivista Del Nuovo Cimento Series 3 12, no. 10 (October 1989): 1–112. http://dx.doi.org/10.1007/bf02740010.

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13

FODA, OMAR. "MOMENTUM-SUBTRACTION RENORMALIZATION TECHNIQUES IN CURVED SPACE-TIME." International Journal of Modern Physics A 02, no. 05 (October 1987): 1549–65. http://dx.doi.org/10.1142/s0217751x87000818.

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Momentum-subtraction techniques, specifically BPHZ and Zimmermann’s Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.

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14

VARADARAJAN, MADHAVAN. "QUANTUM CYLINDRICAL WAVES AND PARAMETRIZED FIELD THEORY." International Journal of Modern Physics D 15, no. 10 (October 2006): 1743–52. http://dx.doi.org/10.1142/s0218271806009078.

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In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space–time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space–time and review the relevant results for unitary implementability.

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15

Boulware, David G. "Aspects of Quantum Field Theory in Curved Space-Time (S. A. Fulling)." SIAM Review 33, no. 3 (September 1991): 508. http://dx.doi.org/10.1137/1033129.

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16

Odintsov, S. D. "Two-loop effective potential in quantum field theory in curved space-time." Physics Letters B 306, no. 3-4 (June 1993): 233–36. http://dx.doi.org/10.1016/0370-2693(93)90073-q.

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17

BENINI, MARCO, CLAUDIO DAPPIAGGI, and THOMAS-PAUL HACK. "QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER." International Journal of Modern Physics A 28, no. 17 (July 10, 2013): 1330023. http://dx.doi.org/10.1142/s0217751x13300238.

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Goal of this paper is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, it is assigned to a physical system a suitable algebra of observables, which is meant to encode all algebraic relations among observables, such as commutation relations. In the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.

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18

Buchbinder, I. L. "Renormalization of Quantum Field Theory in Curved Space-Time and Renormalization Group Equations." Fortschritte der Physik 34, no. 9 (1986): 605–28. http://dx.doi.org/10.1002/prop.19860340902.

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19

Buchbinder, I. L. "Renormalization of Quantum Field Theory in Curved Space-Time and Renormalization Group Equations." Fortschritte der Physik/Progress of Physics 34, no. 9 (1986): 605–28. http://dx.doi.org/10.1002/prop.2190340902.

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20

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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21

Radzikowski, Marek J., and Rainer Verch. "A local-to-global singularity theorem for quantum field theory on curved space-time." Communications in Mathematical Physics 180, no. 1 (September 1996): 1–22. http://dx.doi.org/10.1007/bf02101180.

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22

Bukhbinder, I. L., and I. L. Shapiro. "Renormalization of a quantum field theory model in a curved space-time with torsion." Soviet Physics Journal 28, no. 8 (August 1985): 685–89. http://dx.doi.org/10.1007/bf00895176.

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23

Hwang, Jai-chan. "Curved space quantum scalar field theory with accompanying metric fluctuations." Physical Review D 48, no. 8 (October 15, 1993): 3544–56. http://dx.doi.org/10.1103/physrevd.48.3544.

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24

Kontsevich, Maxim, and Graeme Segal. "Wick Rotation and the Positivity of Energy in Quantum Field Theory." Quarterly Journal of Mathematics 72, no. 1-2 (June 1, 2021): 673–99. http://dx.doi.org/10.1093/qmath/haab027.

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Abstract We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary Riemannian metrics are contained in the allowable domain, while Lorentzian metrics lie on its boundary.

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25

Ghiti, M. F., N. Mebarki, and H. Aissaoui. "Quantum entanglement of fermions–antifermions pair creation modes in noncommutative Bianchi I space–time." International Journal of Modern Physics A 30, no. 24 (August 28, 2015): 1550141. http://dx.doi.org/10.1142/s0217751x15501419.

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The noncommutative Bianchi I curved space–time vierbeins and spin connections are derived. Moreover, the corresponding noncommutative Dirac equation as well as its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann fermion–antifermion pair creation quantum entanglement entropy is studied. It is shown that its behavior is strongly dependent on the value of the noncommutativity [Formula: see text] parameter, [Formula: see text]-modes frequencies and the structure of the curved space–time. Various discussions of the obtained features are presented.

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26

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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27

Radzikowski, Marek J. "Micro-local approach to the Hadamard condition in quantum field theory on curved space-time." Communications in Mathematical Physics 179, no. 3 (September 1996): 529–53. http://dx.doi.org/10.1007/bf02100096.

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28

Mir-Kasimov, R. M. "Singular Functions in Quantum Field Theory with De Sitter Momentum Space." International Journal of Modern Physics A 12, no. 01 (January 10, 1997): 255–58. http://dx.doi.org/10.1142/s0217751x97000372.

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The positive frequency part of commutation Pauli-Jordan function in the Quantum Field Theory with curved momentum space or Quantum configurational space is calculated in explicit form for scalar field. The expressions for other siigular functions are also written in terms of Legendre functions

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29

Santos, A. F., S. C. Ulhoa, and Faqir C. Khanna. "On Stefan–Boltzmann law and the Casimir effect at finite temperature in the Schwarzschild space–time." International Journal of Modern Physics A 35, no. 13 (May 10, 2020): 2050066. http://dx.doi.org/10.1142/s0217751x20500669.

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This paper deals with quantum field theory in curved space–time using the Thermo Field Dynamics. The scalar field is coupled to the Schwarzschild space–time and then thermalized. The Stefan–Boltzmann law is established at finite temperature and the entropy of the field is calculated. Then the Casimir energy and pressure are obtained at zero and finite temperature.

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30

Matsutani, Shigeki. "Quantum field theory on curved low-dimensional space embedded in three-dimensional space." Physical Review A 47, no. 1 (January 1, 1993): 686–89. http://dx.doi.org/10.1103/physreva.47.686.

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31

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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32

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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33

CANARUTTO, DANIEL. "QUANTUM BUNDLES AND QUANTUM INTERACTIONS." International Journal of Geometric Methods in Modern Physics 02, no. 05 (October 2005): 895–917. http://dx.doi.org/10.1142/s0219887805000855.

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A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles ("quantum bundles") over the space–time manifold yield a quantum "formalism" along any 1-dimensional timelike submanifold (a "detector"); in the flat, inertial case this reproduces the basic results of the usual quantum field theory, while in general it could be seen as a local, "linearized" description of the actual physics.

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34

HENNINGSON, MÅNS. "DUALITY OF STRING AMPLITUDES IN A CURVED BACKGROUND." International Journal of Modern Physics A 08, no. 30 (December 10, 1993): 5409–40. http://dx.doi.org/10.1142/s0217751x93002150.

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We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the SU(2) group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field-theoretical amplitude. The corresponding string theory calculation is performed for a special case, and we discuss how more general string theory amplitudes could be evaluated.

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35

Oldani, Richard. "Quantum gravity for dummies." Physics Essays 34, no. 1 (March 14, 2021): 1–2. http://dx.doi.org/10.4006/0836-1398-34.1.1.

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Dirac noted in his first paper on quantum electrodynamics [Proc. Roy. Soc. A 114, 243 (1927)] that, “The theory is non-relativistic only on account of the time being counted throughout as a c-number [classically], instead of being treated symmetrically with the space coordinates.” His suggestion for a relativistic theory of quantum mechanics is carried out here by describing the atom in configuration space as the action integral of a Lagrangian. Atomic structure is described with discrete coordinates in Minkowski space, while the atom itself resides in the curved space-time continuum of the gravitational field, the background space of quantum gravity. Although it does not meet the more ambitious goals of a string theory or loop quantum gravity, it is the first successful theory. In other words, it is the first theory to describe how gravitational fields interact with quanta at the microscopic level. This paper is dedicated to the thousands of theoretical physicists who have defended nonrelativistic theory since its inception in 1926 without questioning its limitations even as it lost touch with reality and became ever more difficult to believe.

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36

CALIXTO, M., V. ALDAYA, and M. NAVARRO. "QUANTUM FIELD THEORY IN A SYMMETRIC CURVED SPACE FROM A SECOND QUANTIZATION ON A GROUP." International Journal of Modern Physics A 15, no. 25 (October 10, 2000): 4011–44. http://dx.doi.org/10.1142/s0217751x00001233.

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In this paper we propose a "second quantization" scheme especially suitable for dealing with nontrivial, highly symmetric phase spaces, implemented within a more general group approach to quantization, which recovers the standard quantum field theory (QFT) for ordinary relativistic linear fields. We emphasize, among its main virtues, greater suitability in characterizing vacuum states in a QFT on a highly symmetric curved space–time and the absence of the usual requirement of global hyperbolicity. This can be achieved in the special case of the Anti-de Sitter universe, on which we explicitly construct a QFT.

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37

NIKOLIĆ, HRVOJE. "HORAVA–LIFSHITZ GRAVITY, ABSOLUTE TIME, AND OBJECTIVE PARTICLES IN CURVED SPACE." Modern Physics Letters A 25, no. 19 (June 21, 2010): 1595–601. http://dx.doi.org/10.1142/s0217732310033359.

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Recently, Horava formulated a renormalizable theory of quantum gravity that reduces to general relativity at large distances but violates Lorentz invariance at small distances. The absolute time involved in this theory allows to define an objective notion of particles associated with quantization of fields in classical gravitational backgrounds. The Unruh effect and other observer-dependent notions of particles in curved space are interpreted as effects caused by interaction between the objective vacuum and the measuring apparatus made up of objective particles.

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38

Fonarev, Oleg A. "Wigner function and quantum kinetic theory in curved space–time and external fields." Journal of Mathematical Physics 35, no. 5 (May 1994): 2105–29. http://dx.doi.org/10.1063/1.530542.

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39

BANDER, MYRON. "QUANTUM MECHANICS AND FIELD THEORY WITH MOMENTUM DEFINED ON AN ANTI-DE SITTER SPACE." International Journal of Modern Physics A 25, no. 26 (October 20, 2010): 4889–99. http://dx.doi.org/10.1142/s0217751x10050810.

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Relativistic dynamics with energy and momentum restricted to an anti-de Sitter space is presented. Coordinate operators conjugate to such momenta are introduced. Definition of functions of these operators, their differentiation and integration, all necessary for the development of dynamics is presented. The resulting algebra differs from the standard Heisenberg one, notably in that the space–time coordinates do not commute among each other. The resulting time variable is discrete and the limit to continuous time presents difficulties. A parallel approach, in which an overlap function, between position and momentum states, is obtained from solutions of wave equations on this curved space are also investigated. This approach, likewise, has problems in the that high energy behavior of these overlap functions precludes a space–time definition of action functionals.

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40

Audretsch, J. "S-matrix approach to interacting quantum field theory in curved space-time1)." Astronomische Nachrichten: A Journal on all Fields of Astronomy 307, no. 5 (1986): 261–65. http://dx.doi.org/10.1002/asna.2113070502.

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41

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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42

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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43

KOCH, BENJAMIN. "HIGHER-DIMENSIONAL GEOMETRIC DESCRIPTION OF THE QUANTUM KLEIN–GORDON EQUATION." International Journal of Geometric Methods in Modern Physics 10, no. 09 (August 30, 2013): 1320014. http://dx.doi.org/10.1142/s0219887813200144.

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It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.

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Nieuwenhuizen, Theo M., and V. Špička. "Bose–Einstein condensed supermassive black holes: A case of renormalized quantum field theory in curved space–time." Physica E: Low-dimensional Systems and Nanostructures 42, no. 3 (January 2010): 256–68. http://dx.doi.org/10.1016/j.physe.2009.10.040.

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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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Kanatchikov, Igor V. "Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time." Symmetry 11, no. 11 (November 15, 2019): 1413. http://dx.doi.org/10.3390/sym11111413.

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The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended to arbitrary curved space-times. In the limiting case when the inverse of the ultraviolet parameter ϰ introduced by precanonical quantization is mapped to the infinitesimal invariant spatial volume element, the canonical functional derivative Schrödinger equation is derived from the manifestly covariant partial derivative precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional spatial product integral of Clifford-algebra-valued precanonical wave function or the product integral of a scalar function obtained from the precanonical wave function by a sequence of transformations. In non-static space-times, the transformations include a nonlocal transformation given by the time-ordered exponential of the zero-th component of spin-connection.

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47

Baker, Daniel, Darsh Kodwani, Ue-Li Pen, and I.-Sheng Yang. "A self-consistency check for unitary propagation of Hawking quanta." International Journal of Modern Physics A 32, no. 33 (November 30, 2017): 1750198. http://dx.doi.org/10.1142/s0217751x17501986.

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The black hole information paradox presumes that quantum field theory in curved space–time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space–time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in QFT might be related to a solution of the paradox based on the soft-hair-memory effect.

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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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Fulling, S. A. "Curved Space Quantum Field Theory of the 1970S Elucidates Boundary Casimir Energy Today." Russian Physics Journal 59, no. 11 (March 2017): 1804–6. http://dx.doi.org/10.1007/s11182-017-0979-9.

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50

Ipek, Selman, and Ariel Caticha. "The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity." Symmetry 12, no. 8 (August 7, 2020): 1324. http://dx.doi.org/10.3390/sym12081324.

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Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

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