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1

Medina, Julieta, and Denjoe O'Connor. "Scalar field theory on fuzzyS4." Journal of High Energy Physics 2003, no. 11 (November 21, 2003): 051. http://dx.doi.org/10.1088/1126-6708/2003/11/051.

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2

Tiwari, S. C. "Scalar field in gravitational theory." Physics Letters A 142, no. 8-9 (December 1989): 460–64. http://dx.doi.org/10.1016/0375-9601(89)90514-8.

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3

Horndeski, Gregory W. "The hidden scalar Lagrangians within Horndeski theory." International Journal of Modern Physics D 29, no. 14 (September 9, 2020): 2043004. http://dx.doi.org/10.1142/s021827182043004x.

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In this paper, I show that there exists a new way to obtain scalar–tensor field theories by combining a special scalar field on the cotangent bundle with a scalar field on spacetime. These two scalar fields act as a generating function for the metric tensor. When using these two scalar fields in the Horndeski Lagrangians, we discover, while seeking Friedmann–Lemaître–Robertson–Walker-type cosmological solutions, that hidden in the Horndeski Lagrangians are nondegenerate second-order scalar Lagrangians. In accordance with Ostrogradsky’s work, these hidden scalar Lagrangians lead to multiple vacuum solutions, and thereby predict the existence of the multiverse. The multiverse is comprised of numerous different types of individual universes. For example, some begin explosively, and then coast along exponentially forever at an accelerated rate, while others begin in that manner, and then stop expanding and contract.
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4

Nesnov, Dmitry. "Field theory in normal conical coordinates." E3S Web of Conferences 244 (2021): 09004. http://dx.doi.org/10.1051/e3sconf/202124409004.

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In the scientific literature, the field theory is most fully covered in the cylindrical and spherical coordinate systems. This is explained by the fact that the mathematical apparatus of these systems is most well studied. When the source of field has a more complex structure than a point or a straight line, there is a need for new approaches to their study. The goal of this research is to adapt the field theory related to curvilinear coordinates in order to represent it in the normal conical coordinates. In addition, an important part of the research is the development of a geometrical modeling apparatus for scalar and vector field level surfaces using computer graphics. The paper shows the dependences of normal conical coordinates on rectangular Cartesian coordinates, Lame coefficients. The differential characteristics of the scalar and vector fields in normal conical coordinates are obtained: Laplacian of scalar and vector fields, divergence, rotation of the vector field. The example case shows the features of the application of the mathematical apparatus of geometrical field modeling in normal conical coordinates. For the first time, expressions for the characteristics of the scalar and vector fields in normal conical coordinates are obtained. Methods for geometrical modeling of fields using computer graphics have been developed to provide illustration in their study.
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5

Geng, Chao-Qiang, Hao-Jui Kuan, and Ling-Wei Luo. "Viable constraint on scalar field in scalar–tensor theory." Classical and Quantum Gravity 37, no. 11 (May 6, 2020): 115001. http://dx.doi.org/10.1088/1361-6382/ab86fb.

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6

HESS, PETER O., and WALTER GREINER. "PSEUDO-COMPLEX FIELD THEORY." International Journal of Modern Physics E 16, no. 06 (July 2007): 1643–79. http://dx.doi.org/10.1142/s0218301307006964.

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A new formulation of field theory is presented, based on a pseudo-complex description. An extended group structure is introduced, implying a minimal scalar length, rendering the theory regularized a la Pauli–Villars. Cross sections are calculated for the scattering of an electron at an external Coulomb field and the Compton scattering. Deviations due to a smallest scalar length are determined. The theory also permits a modification of the minimal coupling scheme, resulting in a generalized dispersion relation. A shift of the Greisen–Zatsepin–Kuzmin (GZK) limit of the cosmic ray spectrum is the consequence.
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7

Strickland, Michael. "Reorganizing Finite Temperature Field Theory: Part I.: Scalar Field Theory." International Journal of Modern Physics A 16, supp01c (September 2001): 1277–80. http://dx.doi.org/10.1142/s0217751x01009521.

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I present a method for self-consistently including the effects of screening in finite-temperature field theory calculations. The method reproduces the perturbative limit in the weak-coupling limit and for intermediate couplings this method has much better convergence than standard perturbation theory. The method relies on a reorganization of perturbation theory accomplished by shifting the expansion point used to calculate quantum loop corrections. I will present results from a three-loop calculation within this formalism for scalar λϕ4.
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8

LIU, HONGYA, and PAUL S. WESSON. "KALUZA–KLEIN–GORDON FIELD THEORY." International Journal of Modern Physics D 07, no. 05 (October 1998): 737–47. http://dx.doi.org/10.1142/s0218271898000498.

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We extend the induced-matter interpretation of Kaluza–Klein field theory to obtain the Klein–Gordon equation for a scalar particle. The motion of the particle is correctly recovered, and we give an exact plane-wave solution whose induced energy-momentum tensor depends only on first derivatives of the scalar field, as in flat-space quantum field theory. However, in general the energy and momenta of the particle also include terms in second derivatives, which should repay investigation.
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9

Chernitskii, Alexander. "Gravitation in Unified Scalar Field Theory." Universe 7, no. 1 (January 9, 2021): 11. http://dx.doi.org/10.3390/universe7010011.

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The scalar field of space-time film is considered as unified fundamental field. The field model under consideration is the space-time generalization of the model for a two-dimensional thin film. The force and metrical interactions between solitons are considered. These interactions correspond to the electromagnetic and gravitational interactions respectively. The metrical interaction and its correspondence to the gravitational one are considered in detail. The practical applications of this approach are briefly discussed.
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10

Chernitskii, Alexander A. "Gravitation in Unified Scalar Field Theory." Universe 7, no. 1 (January 9, 2021): 11. http://dx.doi.org/10.3390/universe7010011.

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The scalar field of space-time film is considered as unified fundamental field. The field model under consideration is the space-time generalization of the model for a two-dimensional thin film. The force and metrical interactions between solitons are considered. These interactions correspond to the electromagnetic and gravitational interactions respectively. The metrical interaction and its correspondence to the gravitational one are considered in detail. The practical applications of this approach are briefly discussed.
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11

LOEWE, M., and C. VALENZUELA. "THERMAL RENORMALONS IN SCALAR FIELD THEORY." Modern Physics Letters A 15, no. 18 (June 14, 2000): 1181–90. http://dx.doi.org/10.1142/s0217732300001481.

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In the framework of the scalar theory gϕ4, we explore the occurrence of thermal renormalons, i.e. temperature-dependent singularities in the Borel plane. The discussion of a particular renormalon type diagram at finite temperature, using Thermofield Dynamics, allows us to establish that these singularities actually get a temperature dependence. This dependence appears in the residues of the poles, the positions of the poles remain unchanged with temperature.
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12

Huang, Kerson, Chi Xiong, and Xiaofei Zhao. "Scalar-field theory of dark matter." International Journal of Modern Physics A 29, no. 13 (May 15, 2014): 1450074. http://dx.doi.org/10.1142/s0217751x14500742.

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We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein–Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.
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13

de Goursac, Axel, and Jean-Christophe Wallet. "Symmetries of noncommutative scalar field theory." Journal of Physics A: Mathematical and Theoretical 44, no. 5 (January 4, 2011): 055401. http://dx.doi.org/10.1088/1751-8113/44/5/055401.

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14

Hertzberg, Mark P. "Entanglement entropy in scalar field theory." Journal of Physics A: Mathematical and Theoretical 46, no. 1 (December 6, 2012): 015402. http://dx.doi.org/10.1088/1751-8113/46/1/015402.

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15

Wang, Enke, Ulrich Heinz, and Xiaofei Zhang. "Viscosity in hot scalar field theory." Physical Review D 53, no. 10 (May 15, 1996): 5978–81. http://dx.doi.org/10.1103/physrevd.53.5978.

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16

Norbury, John W., Frank Dick, Ryan B. Norman, and Khin Maung Maung. "Cross-sections from scalar field theory." Canadian Journal of Physics 88, no. 3 (March 2010): 149–56. http://dx.doi.org/10.1139/p10-002.

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A scalar quantum field theory method is used to calculate differential and total cross-sections for elastic and inelastic scattering in proton–proton collisions. When Mandelstam variables are used, the resulting formulas are simple and can be written in closed form. They display features very typical of elastic and inelastic scattering. The results show good agreement with total cross-section data for η meson production. Thus for this particular example, a simple scalar model can be used in place of a more complicated field theory with spin.
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17

GIARDINO, SERGIO, and PAULO TEOTÔNIO-SOBRINHO. "A NONASSOCIATIVE QUATERNION SCALAR FIELD THEORY." Modern Physics Letters A 28, no. 35 (October 30, 2013): 1350163. http://dx.doi.org/10.1142/s0217732313501630.

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A nonassociative Groenewold–Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.
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18

Addazi, Andrea. "Chaotic instantons in scalar field theory." International Journal of Geometric Methods in Modern Physics 14, no. 10 (September 13, 2017): 1750135. http://dx.doi.org/10.1142/s0219887817501353.

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We consider a new class of instantons in context of quantum field theory of a scalar field coupled with a chaotic background source field. We show how the instanton associated to the quantum tunneling from a metastable false to the true vacuum will be corrected by an exponential enhancement factor. Possible implications are discussed.
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19

Hara, Takashi, Tetsuya Hattori, Kei-ichi Kondo, and Hal Tasaki. "Scalar Field Theory from Statistical Mechanics." Progress of Theoretical Physics Supplement 92 (1987): 1–13. http://dx.doi.org/10.1143/ptps.92.1.

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20

Huang, Kerson, Efstratios Manousakis, and Janos Polonyi. "Effective potential in scalar field theory." Physical Review D 35, no. 10 (May 15, 1987): 3187–92. http://dx.doi.org/10.1103/physrevd.35.3187.

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21

Thomas, A. "Ito's theorem and scalar field theory." Journal of Physics A: Mathematical and General 18, no. 13 (September 11, 1985): 2451–55. http://dx.doi.org/10.1088/0305-4470/18/13/021.

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22

Gepner, Doron. "Scalar field theory and string compactification." Nuclear Physics B 322, no. 1 (August 1989): 65–81. http://dx.doi.org/10.1016/0550-3213(89)90485-9.

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23

Cattaruzza, E., E. Gozzi, and A. Francisco Neto. "Diagrammar in classical scalar field theory." Annals of Physics 326, no. 9 (September 2011): 2377–430. http://dx.doi.org/10.1016/j.aop.2011.05.009.

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24

Kar, Arnab, and S. G. Rajeev. "Scalar quantum field theory on fractals." Annals of Physics 327, no. 1 (January 2012): 102–17. http://dx.doi.org/10.1016/j.aop.2011.10.008.

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25

Ball, R. D., and R. S. Thorne. "Renormalizability of Effective Scalar Field Theory." Annals of Physics 236, no. 1 (November 1994): 117–204. http://dx.doi.org/10.1006/aphy.1994.1109.

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26

COSTA, K. M. "SCALAR FIELD THEORY ON A KÄHLER MANIFOLD." Modern Physics Letters A 04, no. 12 (June 20, 1989): 1127–34. http://dx.doi.org/10.1142/s0217732389001301.

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The invariant one-loop counter terms for a class of non-polynomial complex scalar field theories are found using the background field geodesic expansion together with heat kernel methods. These theories have dynamics invariant under a group G with fields that transform linearly only under a subgroup H of G. The fields are coordinates on a complex Kählerian manifold corresponding to the coset space G/H. The technique is applied to the CP n model.
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27

Sharif, M., and Amal Majid. "Complexity factors for static axial system in self-interacting Brans–Dicke gravity." International Journal of Geometric Methods in Modern Physics 16, no. 11 (November 2019): 1950174. http://dx.doi.org/10.1142/s0219887819501743.

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This paper explores the physical attributes of a static axial source that induce complexity within the fluid in the background of self-interacting Brans–Dicke theory. Bel’s approach is used to split the Riemann tensor and construct structure scalars that involve physical features of the fluid in the presence of scalar field. Using the evolution equations derived from Bianchi identities as well as structure scalars, five complexity factors are identified which include constraints on the scalar field. Finally, the conditions of vanishing complexity are used to present solutions for an anisotropic inhomogeneous spheroid. It is concluded that scalar field is an additional source of complexity.
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28

Trinchero, R. "Examples of reflection positive field theories." International Journal of Geometric Methods in Modern Physics 15, no. 02 (January 24, 2018): 1850022. http://dx.doi.org/10.1142/s0219887818500226.

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The requirement of reflection positivity (RP) for Euclidean field theories is considered. This is done for the cases of a scalar field, a higher derivative scalar field theory and the scalar field theory defined on a non-integer dimensional space (NIDS). It is shown that regarding RP, the analytical structure of the corresponding Schwinger functions plays an important role. For the higher derivative scalar field theory, RP does not hold. However for the scalar field theory on a NIDS, RP holds in a certain range of dimensions where the corresponding Minkowskian field is defined on a Hilbert space with a positive definite scalar product that provides a unitary representation of the Poincaré group. In addition, and motivated by the last example, it is shown that, under certain conditions, one can construct non-local reflection positive Euclidean field theories starting from the corrected two point functions of interacting local field theories.
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29

Nesnov, Dmitry V. "Field theory in normal toroidal coordinates." MATEC Web of Conferences 193 (2018): 03022. http://dx.doi.org/10.1051/matecconf/201819303022.

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Field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems has been thoroughly studied. Sources of field with more complex structures require new approaches to their study. The purpose of this research is to adapt the field theory referred to curvilinear coordinates and represent it in normal toroidal coordinates. Another purpose is to develop the foundations of geometric modeling with the use of computer graphics for visualizing the level surfaces. The dependence of normal toroidal coordinates on rectangular Cartesian coordinates and Lame coefficients is shown in this scientific paper. Differential characteristics of scalar and vector fields in normal toroidal coordinates are obtained: scalar and vector field laplacians, divergence, and rotation of vector field. The example shows the technique of modeling the field and its further computer visualization. The technique of reading the internal equation of the surface is presented and the influence of the values of the parameters on the shape of the surface is shown. For the first time, expressions of scalar and vector field characteristics in normal toroidal coordinates are obtained, the fundamentals of geometric modeling of fields with the use of computer graphics tools are developed for the purpose of providing visibility for their study.
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30

KIM, YONG-WAN, YUN SOO MYUNG, and YOUNG-JAI PARK. "BRST QUANTIZATION OF A SIXTH-ORDER DERIVATIVE SCALAR FIELD THEORY." Modern Physics Letters A 28, no. 39 (December 16, 2013): 1350182. http://dx.doi.org/10.1142/s0217732313501824.

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We study a sixth-order derivative scalar field model in Minkowski spacetime as a toy model of higher-derivative critical gravity theories. This model is consistently quantized when using the Becchi–Rouet–Stora–Tyutin (BRST) quantization scheme even though it does not show gauge symmetry manifestly. Imposing a BRST quartet generated by two scalars and ghosts, there remains a nontrivial subspace with positive norm. This might be interpreted as a Minkowskian dual version of the unitary truncation in the logarithmic conformal field theory.
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31

PEREZ BERGLIAFFA, S. E., and K. E. HIBBERD. "INHOMOGENEOUS SCALAR FIELD SOLUTIONS AND INFLATION." International Journal of Modern Physics D 08, no. 06 (December 1999): 705–18. http://dx.doi.org/10.1142/s0218271899000511.

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We present new exact cosmological inhomogeneous solutions for gravity coupled to a scalar field in a general framework specified by the parameter λ. The equations of motion (and consequently the solutions) in this framework correspond to either low-energy string theory or Weyl integrable spacetime according to the sign of λ. We show that different inflationary behaviors are possible, as suggested by the study of the violation of the strong energy condition. Finally, by the analysis of certain curvature scalars we found that some of the solutions may be nonsingular.
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32

LANGFELD, KURT, and HUGO REINHARDT. "ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICE." Modern Physics Letters A 13, no. 31 (October 10, 1998): 2495–501. http://dx.doi.org/10.1142/s0217732398002655.

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A scalar field theory in four space–time dimensions is proposed, which embodies a scalar condensate, but is free of the conceptual problems of standard ϕ4-theory. We propose an N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The scalar lattice model is analytically solved in the large-N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle. The model might serve as an alternative to the Higgs sector of the standard model, where the quantum level of the standard ϕ4-theory contradicts phenomenology due to triviality.
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33

Li, Tianjun, Zhijin Li, and Dimitri V. Nanopoulos. "Helical Phase Inflation and Monodromy in Supergravity Theory." Advances in High Energy Physics 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/397410.

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We study helical phase inflation which realizes “monodromy inflation” in supergravity theory. In the model, inflation is driven by the phase component of a complex field whose potential possesses helicoid structure. We construct phase monodromy based on explicitly breaking globalU(1)symmetry in the superpotential. By integrating out heavy fields, the phase monodromy from single complex scalar field is realized and the model fulfills natural inflation. The phase-axion alignment is achieved from explicitly symmetry breaking and gives super-Planckian phase decay constant. TheF-term scalar potential provides strong field stabilization for all the scalars except inflaton, which is protected by the approximate globalU(1)symmetry. Besides, we show that helical phase inflation can be naturally realized in no-scale supergravity withSU(2,1)/SU(2)×U(1)symmetry since the supergravity setup needed for phase monodromy is automatically provided in the no-scale Kähler potential. We also demonstrate that helical phase inflation can be reduced to another well-known supergravity inflation model with shift symmetry. Helical phase inflation is free from the UV-sensitivity problem although there is super-Planckian field excursion, and it suggests that inflation can be effectively studied based on supersymmetric field theory while a UV-completed framework is not prerequisite.
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34

KERIMOV, G. A. "SCALAR FIELD THEORY IN THE AdS/CFT CORRESPONDENCE: AN OPERATOR FORMULATION." Modern Physics Letters A 22, no. 30 (September 28, 2007): 2287–95. http://dx.doi.org/10.1142/s0217732307022487.

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Starting with a scalar field theory in Euclidean anti-de Sitter space constructed in an earlier paper, we examine the boundary limit of the quantized bulk field. Our AdS/CFT correspondence is generally valid for interacting fields, and is illustrated by a treatment of three-point function for scalar fields of arbitrary mass.
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35

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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36

Socorro, J., and J. Juan Rosales. "Quantum Fractionary Cosmology: K-Essence Theory." Universe 9, no. 4 (April 13, 2023): 185. http://dx.doi.org/10.3390/universe9040185.

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Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann–Lemaı^tre–Robertson–Walker (FLRW) model (radiation and inflation-like epochs, for example), appears naturally. In the classical analysis, the kinetic energy of scalar fields can falsify the standard matter in the sense that we obtain the time behavior for the scale factor in all scenarios of our Universe by using the Hamiltonian formalism, where the results are analogous to those obtained by an algebraic procedure in the Einstein field equations with standard matter. In the case of the quantum Wheeler–DeWitt (WDW) equation for the scalar field ϕ, a fractional differential equation of order β=2α2α−1 is obtained. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; that is to say, when ωX∈[0,1], the order belongs to the interval 1≤β≤2, and when ωX∈[−1,0), the order belongs to the interval 0<β≤1. The corresponding quantum solutions are also given.
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37

Gao, Xian, Masahide Yamaguchi, and Daisuke Yoshida. "Higher derivative scalar-tensor theory through a non-dynamical scalar field." Journal of Cosmology and Astroparticle Physics 2019, no. 03 (March 4, 2019): 006. http://dx.doi.org/10.1088/1475-7516/2019/03/006.

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38

MACÍAS, A., and H. DEHNEN. "DIRAC FIELD IN THE FIVE-DEMENSIONAL KALUZA-KLEIN THEORY WITH SCALAR FIELD." International Journal of Modern Physics A 07, no. 21 (August 20, 1992): 5105–13. http://dx.doi.org/10.1142/s0217751x92002325.

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In this work we investigate the five-dimensional Kaluza-Klein theory with a scalar field contained in the metric, where a Dirac-field is coupled to the metric field. We find that in the four-dimensional theory a nontrivial ground state for the scalar field exists and therefore the mass term in the Dirac equation can be interpreted, for example, as the electron mass.
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39

WANG XIN-YI and ZHAO NAN. "NEW SOLITONS IN COUPLED SCALAR FIELD THEORY." Acta Physica Sinica 40, no. 3 (1991): 359. http://dx.doi.org/10.7498/aps.40.359.

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40

Radovskaya, A. A., and A. G. Semenov. "Shear Viscosity of Nonequilibrium Scalar Field Theory." Physics of Particles and Nuclei 52, no. 4 (July 2021): 564–68. http://dx.doi.org/10.1134/s106377962104050x.

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41

SFONDRINI, ALESSANDRO, and TIM A. KOSLOWSKI. "FUNCTIONAL RENORMALIZATION OF NONCOMMUTATIVE SCALAR FIELD THEORY." International Journal of Modern Physics A 26, no. 23 (September 20, 2011): 4009–51. http://dx.doi.org/10.1142/s0217751x11054048.

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In this paper we apply the Functional Renormalization Group Equation (FRGE) to the noncommutative scalar field theory proposed by Grosse and Wulkenhaar. We derive the flow equation in the matrix representation and discuss the theory space for the self-dual model. The features introduced by the external dimensionful scale provided by the noncommutativity parameter, originally pointed out in R. Gurau and O. J. Rosten, J. High Energy Phys.0907, 064 (2009), are discussed in the FRGE context. Using a technical assumption, but without resorting to any truncation, it is then shown that the theory is asymptotically safe for suitably small values of the ϕ4coupling, recovering the result of M. Disertori et al., Phys. Lett. B649, 95 (2007). Finally, we show how the FRGE can be easily used to compute the one-loop beta-functions of the duality covariant model.
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42

CARRILLO-IBARRA, ILIANA, HUGO GARCÍA-COMPEÁN, and FRANCISCO J. TURRUBIATES. "DISSIPATIVE SCALAR FIELD THEORY VIA DEFORMATION QUANTIZATION." International Journal of Modern Physics A 28, no. 16 (June 28, 2013): 1350068. http://dx.doi.org/10.1142/s0217751x13500681.

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The dissipative scalar field theory by means of the deformation quantization formalism is studied. Following the ideas presented by G. Dito and F. J. Turrubiates [Phys. Lett. A352, 309 (2006)] for quantum mechanics, a star product which contains the dissipative effect for the damped oscillation modes of the field is constructed. Employing this approach the expectation values of some observables in the quantum mechanical case as well as certain correlation functions for the field case are obtained under a particular dissipative process.
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43

Akbar, M. M., and E. Woolgar. "Ricci solitons and Einstein-scalar field theory." Classical and Quantum Gravity 26, no. 5 (February 17, 2009): 055015. http://dx.doi.org/10.1088/0264-9381/26/5/055015.

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44

Koniuk, Roman, and Rolf Tarrach. "Scalar field theory in 3+1 dimensions." Physical Review D 31, no. 12 (June 15, 1985): 3178–82. http://dx.doi.org/10.1103/physrevd.31.3178.

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45

Ho, Pei-Ming, and Yi-Ya Tian. "UV-finite scalar field theory with unitarity." Journal of High Energy Physics 2005, no. 01 (January 18, 2005): 026. http://dx.doi.org/10.1088/1126-6708/2005/01/026.

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46

Rochev, V. E. "Asymptotic behavior in the scalar field theory." Journal of Physics A: Mathematical and Theoretical 44, no. 30 (June 23, 2011): 305403. http://dx.doi.org/10.1088/1751-8113/44/30/305403.

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47

Gurau, Razvan, and Oliver J. Rosten. "Wilsonian renormalization of noncommutative scalar field theory." Journal of High Energy Physics 2009, no. 07 (July 17, 2009): 064. http://dx.doi.org/10.1088/1126-6708/2009/07/064.

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48

Brandt, F. T., and J. Frenkel. "Multiparticle tree amplitudes in scalar field theory." Physical Review D 53, no. 4 (February 15, 1996): 2256–59. http://dx.doi.org/10.1103/physrevd.53.2256.

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49

Aarts, Gert, Gian Franco Bonini, and Christof Wetterich. "On thermalization in classical scalar field theory." Nuclear Physics B 587, no. 1-3 (October 2000): 403–18. http://dx.doi.org/10.1016/s0550-3213(00)00447-8.

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50

BRANDT, F. T., J. FRENKEL, and A. GUERRA. "THE BOLTZMANN EQUATION IN SCALAR FIELD THEORY." International Journal of Modern Physics A 13, no. 24 (September 30, 1998): 4281–88. http://dx.doi.org/10.1142/s0217751x98002067.

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Abstract:
We derive the classical transport equation, in scalar field theory with a g2V(ϕ) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action Γ which generates all the n-point Green functions in the high-temperature limit. An explicit and closed form is given for Γ in the static case.
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