Stress tensor and conformal anomalies for massless fields in a Robertson–Walker universe

1977 ◽  
Vol 356 (1687) ◽  
pp. 569-574 ◽  
Keyword(s):  
Stress Tensor ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Einstein Universe ◽  
Massless Fields

We derive the unique, local vacuum stress tensor for electromagnetic, neutrino and massless scalar fields propagating in a Robertson─Walker background spacetime. The result is used to compute the numerical coefficients of the conformal trace anomalies from the known values of the Casimir energy in the Einstein universe.

scholarly journals The Casimir energy for scalar field with mixed boundary condition

2018 ◽  
Vol 15 (10) ◽  
pp. 1850172 ◽  
Author(s):  
M. A. Valuyan
Keyword(s):  
Scalar Field ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Regularization Technique ◽  
Massive Scalar Field ◽  
Subtraction Scheme ◽  
First Order

In this study, the first-order radiative correction to the Casimir energy for massive and massless scalar fields confined with mixed boundary conditions (BCs) (Dirichlet–Neumann) between two points in [Formula: see text] theory was computed. Two issues in performing the calculations in this work are essential: to renormalize the bare parameters of the problem, a systematic method was employed, allowing all influences from the BCs to be imported in all elements of the renormalization program. This idea yields our counterterms appeared in the renormalization program to be position-dependent. Using the Box Subtraction Scheme (BSS) as a regularization technique is the other noteworthy point in the calculation. In this scheme, by subtracting the vacuum energies of two similar configurations from each other, regularizing divergent expressions and their removal process were significantly facilitated. All the obtained answers for the Casimir energy with the mixed BC were consistent with well-known physical grounds. We also compared the Casimir energy for massive scalar field confined with four types of BCs (Dirichlet, Neumann, mixed of them and Periodic) in [Formula: see text] dimensions with each other, and the sign and magnitude of their values were discussed.

Remarks on a gravitational analogue of the Casimir effect

2016 ◽  
Vol 25 (09) ◽  
pp. 1641018 ◽  
Author(s):  
V. B. Bezerra ◽  
H. F. Mota ◽  
C. R. Muniz
Keyword(s):  
Scalar Field ◽  
Cosmic String ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
String Tension ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Einstein Universe

We consider the Casimir effect, by calculating the Casimir energy and its corrections for nonzero temperatures, of a massless scalar field in the spacetime with topology [Formula: see text] (Einstein universe) containing an idealized cosmic string. The obtained results confirm the role played by the identifications imposed on the quantum field by boundary conditions arising from the topology of the gravitational field under consideration and illustrate a realization of a gravitational analogue of the Casimir effect. In this backgorund, we show that the vacuum energy can be written as a term which corresponds to the vacuum energy of the massless scalar field in the Einstein universe added by another term that formally corresponds to the vacuum energy of the electromagnetic field in the Einstein universe, multiplied by a parameter associated with the presence of the cosmic string, namely, [Formula: see text], where [Formula: see text] is a constant related to the cosmic string tension, [Formula: see text].

scholarly journals Gravitons in a Casimir box

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich ◽  
Martin Bronte
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Chemical Potential ◽  
Finite Size ◽  
Neumann Boundary ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Analytical Control ◽  
Slab Geometry

Abstract The partition function of gravitons with Casimir-type boundary conditions is worked out. The simplest box that allows one to achieve full analytical control consists of a slab geometry with two infinite parallel planes separated by a distance d. In this setting, linearized gravity, like electromagnetism, is equivalent to two free massless scalar fields, one with Dirichlet and one with Neumann boundary conditions, which in turn may be combined into a single massless scalar with periodic boundary conditions on an interval of length 2d. When turning on a chemical potential for suitably adapted spin angular momentum, the partition function is modular covariant and expressed in terms of an Eisenstein series. It coincides with that for photons. At high temperature, the result provides in closed form all sub-leading finite-size corrections to the standard (gravitational) black body result. More interesting is the low-temperature/small distance expansion where the leading contribution to the partition function is linear in inverse temperature and given in terms of the Casimir energy of the system, whereas the leading contribution to the entropy is proportional to the area and originates from gravitons propagating parallel to the plates.

scholarly journals CASIMIR EFFECT FOR SCALAR FIELDS WITH ROBIN BOUNDARY CONDITIONS IN SCHWARZSCHILD BACKGROUND

2005 ◽  
Vol 20 (06) ◽  
pp. 441-450 ◽  
Author(s):  
M. R. SETARE
Keyword(s):  
Boundary Conditions ◽  
Stress Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Robin Boundary Conditions ◽  
Massless Scalar Field ◽  
Robin Boundary ◽  
Schwarzschild Background

The stress–tensor of a massless scalar field satisfying Robin boundary conditions on two one-dimensional wall in two-dimensional Schwarzschild background is calculated. We show that vacuum expectation value of stress–tensor can be obtained explicitly by Casimir effect, trace anomaly and Hawking radiation.

scholarly journals Failure of mean-field approximation in weakly coupled dilaton gravity

2018 ◽  
Vol 191 ◽  
pp. 07004
Author(s):  
Maxim Fitkevich
Keyword(s):  
Black Hole ◽  
Mean Field ◽  
Direct Calculation ◽  
Scalar Fields ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Massless Scalar ◽  
Dilaton Gravity ◽  
Black Hole Evaporation ◽  
Weakly Coupled

We investigate black hole evaporation in a weakly coupled model of two-dimensional dilaton gravity paying a particular attention to the validity of the semiclassical mean-field approximation. Our model is obtained by adding a reflecting boundary to the celebrated RST model describing N gravitating massless scalar fields to one-loop level. The boundary cuts off the region of strong coupling. Although our model is explicitly weakly coupled, we find that the mean field approximation inevitably fails at the end of black hole evaporation. We propose an alternative semiclassical method aiming at direct calculation of S-matrix elements and illustrate it in a simple shell model.

scholarly journals Radiative correction to the Casimir energy for massive scalar field on a spherical surface

2017 ◽  
Vol 32 (24) ◽  
pp. 1750128 ◽  
Author(s):  
M. A. Valuyan
Keyword(s):  
Scalar Field ◽  
Radiative Correction ◽  
Spherical Surface ◽  
Perturbation Expansion ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Free Theory

In this paper, the first-order radiative correction to the Casimir energy for a massive scalar field in the [Formula: see text] theory on a spherical surface with [Formula: see text] topology was calculated. In common methods for calculating the radiative correction to the Casimir energy, the counter-terms related to free theory are used. However, in this study, by using a systematic perturbation expansion, the obtained counter-terms in renormalization program were automatically position-dependent. We maintained that this dependency was permitted, reflecting the effects of the boundary conditions imposed or background space in the problem. Additionally, along with the renormalization program, a supplementary regularization technique that we named Box Subtraction Scheme (BSS) was performed. This scheme presents a useful method for the regularization of divergences, providing a situation that the infinities would be removed spontaneously without any ambiguity. Analysis of the necessary limits of the obtained results for the Casimir energy of the massive and massless scalar field confirmed the appropriate and reasonable consistency of the answers.

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