Robertson-Walker type model with conformally invariant scalar field with trace-free energy momentum tensor

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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The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8208-z ◽

2020 ◽

Vol 80 (7) ◽

Author(s):

Mirko Serino

Keyword(s):

Field Theory ◽

Correlation Function ◽

Scalar Field ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

General Covariance ◽

Explicit Result ◽

Conformally Invariant ◽

Point Correlation ◽

Point Correlation Function

Abstract We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit evaluation of the Feynman diagrams by tensor reduction. We work by embedding the scalar field theory in a gravitational background consistently with conformal invariance in order to derive all the terms the correlator consists of and all the Ward identities implied by the requirements of general covariance and anomalous Weyl symmetry. We test all these identities numerically in several kinematic configurations. Mathematica notebooks detailing the step-by-step computation are made publicly available through a GitHub repository (https://github.com/mirkos86/4-EMT-correlation-function-in-a-4d-CFT.). To the best of our knowledge, this is the first explicit result for the four-point correlation function of the energy-momentum tensor in a conformal and non supersymmetric field theory which is readily numerically evaluable in any kinematic configuration.

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N=2 SUPERCONFORMAL INTERACTING BOSONIC MODELS

Modern Physics Letters A ◽

10.1142/s021773239200029x ◽

1992 ◽

Vol 07 (04) ◽

pp. 345-356 ◽

Cited By ~ 2

Author(s):

RON COHEN

Keyword(s):

Free Energy ◽

Energy Momentum Tensor ◽

Central Charge ◽

Oriented Graph ◽

Momentum Tensor ◽

Superconformal Algebra ◽

Chiral Algebra ◽

Bosonic Model ◽

Coset Models

Bosonic representations of N=2 superconformal algebra are studied. We show that the free energy momentum tensor decomposes into an orthogonal sum of the interacting bosonic model (IBM) and a coset-like tensors. We define the notion of flags of models and show that the central charge does not decrease along the flags. We examine the conditions for an arbitrary un-oriented graph to form an IBM. We discuss several properties of the chiral algebra of these models and examine the role of the continuous parameters by studying an example. Finally we discuss the relations between these models and the N=2 superconformal coset models.

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Crystal plasticity: The Hamilton-Eshelby stress in terms of the metric in the intermediate configuration

Theoretical and Applied Mechanics ◽

10.2298/tam1201055m ◽

2012 ◽

Vol 39 (1) ◽

pp. 55-69 ◽

Cited By ~ 2

Author(s):

Paolo Mariano

Keyword(s):

Free Energy ◽

Energy Momentum Tensor ◽

Large Strain ◽

Momentum Tensor ◽

Classical Field ◽

Field Theories ◽

Relative Power ◽

Eshelby Stress ◽

Classical Field Theories ◽

Intermediate Configuration

The Hamilton-Eshelby stress is a basic ingredient in the description of the evolution of point, lines and bulk defects in solids. The link between the Hamilton-Eshelby stress and the derivative of the free energy with respect to the material metric in the plasticized intermediate configuration, in large strain regime, is shown here. The result is a modified version of Rosenfeld-Belinfante theorem in classical field theories. The origin of the appearance of the Hamilton-Eshelby stress (the non-inertial part of the energy-momentum tensor) in dissipative setting is also discussed by means of the concept of relative power.

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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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Cosmic acceleration with tachyon field

Modern Physics Letters A ◽

10.1142/s0217732318501997 ◽

2018 ◽

Vol 33 (34) ◽

pp. 1850199 ◽

Cited By ~ 1

Author(s):

A. I. Keskin

Keyword(s):

Scalar Field ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Cosmic Acceleration ◽

Late Time ◽

De Sitter ◽

Tachyon Field ◽

Minimal Coupling ◽

Acceleration Of The Universe ◽

The Universe

In this study, we examine two models of the scalar field, that is, a normal scalar field and a tachyon scalar field in [Formula: see text] gravity to describe cosmic acceleration of the universe, where [Formula: see text], [Formula: see text] and [Formula: see text] are Ricci curvature scalar, trace of energy–momentum tensor and kinetic energy of scalar field [Formula: see text], respectively. Using the minimal-coupling Lagrangian [Formula: see text], for both the scalar models we obtain a viable cosmological system, where [Formula: see text] and [Formula: see text] are real constants. While a normal scalar field gives a system describing expansion from the deceleration to the late-time acceleration, tachyon field together with [Formula: see text] in the system produces a quintessential expansion which is very close to de Sitter point, where we find a new condition [Formula: see text] for inflation.

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The backreaction of massive scalar field on FLRW and de Sitter spaces

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820500334 ◽

2020 ◽

Vol 17 (03) ◽

pp. 2050033

Author(s):

M. R. Setare ◽

M. Sahraee

Keyword(s):

Scalar Field ◽

Energy Momentum Tensor ◽

Friedmann Equation ◽

Vacuum Expectation ◽

Momentum Tensor ◽

Scale Factor ◽

Massive Scalar ◽

De Sitter ◽

Massive Scalar Field ◽

Quantum Energy

In this paper, we obtain the effect of backreaction on the scale factor of the Friedmann–Lemaître–Robertson–Walker (FLRW) and de Sitter spaces. We consider a non-minimally coupled massive scalar field to the curvature scalar. For our purpose, we use the results of vacuum expectation values of energy–momentum tensor, which have been obtained previously. By substituting the quantum energy density into the Friedmann equation, we obtain the linear order perturbation of the scale factor. So, the effect of backreaction leads to the new scale factor.

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