The renormalized energy-momentum tensor and Casimir effect of Dirac field in two-dimensional static spacetime

Liu Cheng-Zhou;  Zhang Chang-Ping

doi:10.7498/aps.56.1928

Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

Advances in High Energy Physics ◽

10.1155/2020/7032834 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

R. G. G. Amorim ◽

S. C. Ulhoa ◽

J. S. da Cruz Filho ◽

A. F. Santos ◽

F. C. Khanna

Keyword(s):

Quantum Mechanics ◽

Phase Space ◽

Finite Temperature ◽

Energy Momentum Tensor ◽

Casimir Effect ◽

Momentum Tensor ◽

Dirac Field ◽

Standard Quantum ◽

Thermo Field Dynamics ◽

Boltzmann Law

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

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Aspects of the BTZ black hole interacting with fields

Modern Physics Letters A ◽

10.1142/s0217732319502511 ◽

2019 ◽

Vol 34 (31) ◽

pp. 1950251

Author(s):

Leonardo Ortíz ◽

Nora Bretón

Keyword(s):

Black Hole ◽

Scalar Field ◽

Heat Kernel ◽

Effective Action ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Three Dimensions ◽

Dirac Field ◽

Btz Black Hole ◽

Renormalized Energy

We show that there is no superradiance for the Dirac field in the rotating BTZ black hole if the field vanishes at infinity. Then we outline the calculation of the expression for the renormalized energy–momentum tensor, the effective action as well as the heat kernel for the Dirac field for the BTZ black hole. Finally, we point out how to construct the Hartle–Hawking–Israel state for the real scalar field in the non-rotating BTZ black hole in two and three dimensions.

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CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

International Journal of Modern Physics D ◽

10.1142/s0218271811018767 ◽

2011 ◽

Vol 20 (02) ◽

pp. 161-168 ◽

Cited By ~ 1

Author(s):

MOHAMMAD R. SETARE ◽

M. DEHGHANI

Keyword(s):

Scalar Field ◽

Energy Momentum Tensor ◽

Casimir Effect ◽

Vacuum Expectation ◽

Robin Boundary Condition ◽

Momentum Tensor ◽

Space Time ◽

Conformally Invariant ◽

Time Space ◽

Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

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Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

Journal of High Energy Physics ◽

10.1007/jhep12(2020)168 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yi Li ◽

Yang Zhou

Keyword(s):

Field Theory ◽

Euclidean Plane ◽

Energy Momentum Tensor ◽

Central Charge ◽

Momentum Tensor ◽

Two Dimensional ◽

Conformal Field ◽

Operator Identity ◽

Pure Gravity ◽

Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

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THE LOCALLY COVARIANT DIRAC FIELD

Reviews in Mathematical Physics ◽

10.1142/s0129055x10003990 ◽

2010 ◽

Vol 22 (04) ◽

pp. 381-430 ◽

Cited By ~ 38

Author(s):

KO SANDERS

Keyword(s):

Energy Momentum Tensor ◽

Momentum Tensor ◽

Dirac Field ◽

Quantum Field ◽

Geometric Constructions ◽

Covariant Quantum ◽

Dimensional Spacetime ◽

Stress Energy ◽

Hadamard States ◽

Stress Energy Momentum Tensor

We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra, the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally, we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

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Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

EPJ Web of Conferences ◽

10.1051/epjconf/201817507013 ◽

2018 ◽

Vol 175 ◽

pp. 07013 ◽

Cited By ~ 6

Author(s):

Yusuke Taniguchi ◽

Shinji Ejiri ◽

Kazuyuki Kanaya ◽

Masakiyo Kitazawa ◽

Asobu Suzuki ◽

...

Keyword(s):

Correlation Function ◽

Finite Temperature ◽

Linear Response ◽

Quark Mass ◽

Energy Momentum Tensor ◽

Gradient Flow ◽

Momentum Tensor ◽

Entropy Density ◽

Tensor Correlation ◽

Renormalized Energy

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.

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Quantum Vacuum Effects in Braneworlds on AdS Bulk

Universe ◽

10.3390/universe6100181 ◽

2020 ◽

Vol 6 (10) ◽

pp. 181

Author(s):

Aram A. Saharian

Keyword(s):

Boundary Condition ◽

Scalar Field ◽

Energy Momentum Tensor ◽

Normal Component ◽

Momentum Tensor ◽

Dirac Field ◽

Curvature Radius ◽

Perfect Conductor ◽

Quantum Vacuum ◽

Local Properties

We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both cases, the contribution in the vacuum expectation value (VEV) of the energy–momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the brane larger than the AdS curvature radius. In the geometry with a brane parallel to the AdS boundary, the VEV of the energy–momentum tensor is considered for scalar field with the Robin boundary condition, for Dirac field with the bag boundary condition and for the electromagnetic field. In the latter case, two types of boundary conditions are discussed. The first one is a generalization of the perfect conductor boundary condition and the second one corresponds to the confining boundary condition used in QCD for gluons. For the geometry of a brane intersecting the AdS boundary, the case of a scalar field is considered. The corresponding energy–momentum tensor, apart from the diagonal components, has nonzero off-diagonal component. As a consequence of the latter, in addition to the normal component, the Casimir force acquires a component parallel to the brane.

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A NEAR HORIZON CFT DUAL FOR KERR–NEWMAN AdS

International Journal of Modern Physics A ◽

10.1142/s0217751x11053663 ◽

2011 ◽

Vol 26 (18) ◽

pp. 3077-3090 ◽

Cited By ~ 11

Author(s):

BRADLY K. BUTTON ◽

LEO RODRIGUEZ ◽

CATHERINE A. WHITING ◽

TUNA YILDIRIM

Keyword(s):

Black Hole ◽

Energy Momentum Tensor ◽

Central Charge ◽

Virasoro Algebra ◽

Momentum Tensor ◽

Two Dimensional ◽

S Wave ◽

One Dimensional ◽

Conformal Field ◽

Asymptotic Symmetries

We show that the near horizon regime of a Kerr–Newman AdS (KNAdS) black hole, given by its two-dimensional analogue a là Robinson and Wilczek (Phys. Rev. Lett.95, 011303 (2005)), is asymptotically AdS2 and dual to a one-dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy–momentum tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein–Hawking entropy via Cardy's formula. Our derived central charge also agrees with the near extremal Kerr/CFT correspondence (Phys. Rev. D80, 124008 (2009)) in the appropriate limits. We also compute the Hawking temperature of the KNAdS black hole by coupling its Robinson and Wilczek two-dimensional analogue (RW2DA) to conformal matter.

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