scholarly journals TRACE ANOMALY AND CASIMIR EFFECT

2000 ◽  
Vol 15 (35) ◽  
pp. 2159-2164 ◽  
Author(s):  
M. R. SETARE ◽  
A. H. REZAEIAN
Keyword(s):  
Boundary Conditions ◽  
Stress Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Casimir Energy ◽  
Two Dimensions ◽  
Dirichlet Boundary Conditions ◽  
Curved Space ◽  
Trace Anomaly ◽  
Dimensional Domain

The Casimir energy for scalar field of two parallel conductors in two-dimensional domain wall background, with Dirichlet boundary conditions, is calculated by making use of general properties of renormalized stress–tensor. We show that vacuum expectation values of stress–tensor contain two terms which come from the boundary conditions and the gravitational background. In two dimensions the minimal coupling reduces to the conformal coupling and stress–tensor can be obtained by the local and nonlocal contributions of the anomalous trace. This work shows that there exists a subtle and deep connection between Casimir effect and trace anomaly in curved space–time.

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 CASIMIR EFFECT IN BACKGROUND OF STATIC DOMAIN WALL

2001 ◽  
Vol 16 (08) ◽  
pp. 1463-1469 ◽  
Author(s):  
M. R. SETARE ◽  
A. SAHARIAN
Keyword(s):  
Domain Wall ◽  
Boundary Conditions ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Dirichlet Boundary Conditions ◽  
Expectation Values ◽  
Plate Geometry ◽  
Gravitational Background

In this paper we investigate the vacuum expectation values of energy–momentum tensor for conformally coupled scalar field in the standard parallel plate geometry with Dirichlet boundary conditions and in the background of planar domain wall case. First we calculate the vacuum expectation values of energy–momentum tensor by using the mode sums, then we show that corresponding properties can be obtained by using the conformal properties of the problem. The vacuum expectation values of energy–momentum tensor contain two terms which come from the boundary conditions and the the gravitational background. In the Minkowskian limit our results agree with those obtained in Ref. 3.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC D-DIMENSIONAL SPHERES

2012 ◽  
Vol 27 (18) ◽  
pp. 1250094 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Complex Plane ◽  
Casimir Force ◽  
Dirichlet Boundary ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel–Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between (D-1)-dimensional surfaces, close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force.

scholarly journals Scalar Casimir effect for a conducting cylinder in a Lorentz-violating background

2021 ◽  
pp. 2150168
Author(s):  
A. M. Escobar-Ruiz ◽  
A. Martín-Ruiz ◽  
C. A. Escobar ◽  
Román Linares
Keyword(s):  
Cylindrical Shell ◽  
Green's Functions ◽  
Green’S Functions ◽  
Casimir Effect ◽  
Normal Component ◽  
Vacuum Expectation ◽  
Dirichlet Boundary Conditions ◽  
Order Differential Operator ◽  
Energy Tensor ◽  
Approximate Analytical Expression

Following a field-theoretical approach, we study the scalar Casimir effect upon a perfectly conducting cylindrical shell in the presence of spontaneous Lorentz symmetry breaking. The scalar field is modeled by a Lorentz-breaking extension of the theory for a real scalar quantum field in the bulk regions. The corresponding Green’s functions satisfying Dirichlet boundary conditions on the cylindrical shell are derived explicitly. We express the Casimir pressure (i.e. the vacuum expectation value of the normal–normal component of the stress–energy tensor) as a suitable second-order differential operator acting on the corresponding Green’s functions at coincident arguments. The divergences are regulated by making use of zeta function techniques, and our results are successfully compared with the Lorentz invariant case. Numerical calculations are carried out for the Casimir pressure as a function of the Lorentz-violating coefficient, and an approximate analytical expression for the force is presented as well. It turns out that the Casimir pressure strongly depends on the Lorentz-violating coefficient and it tends to diminish the force.

scholarly journals Vacuum Expectation Value Profiles of the Bulk Scalar Field in the Generalized Randall-Sundrum Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
A. Tofighi ◽  
M. Moazzen ◽  
A. Farokhtabar
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Cosmological Constant ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Brane World ◽  
Dirichlet Boundary Conditions ◽  
World Model ◽  
Expectation Value ◽  
Bulk Scalar Field

In the generalized Randall-Sundrum warped brane-world model the cosmological constant induced on the visible brane can be positive or negative. In this paper we investigate profiles of vacuum expectation value of the bulk scalar field under general Dirichlet and Neumann boundary conditions in the generalized warped brane-world model. We show that the VEV profiles generally depend on the value of the brane cosmological constant. We find that the VEV profiles of the bulk scalar field for a visible brane with negative cosmological constant and positive tension are quite distinct from those of Randall-Sundrum model. In addition we show that the VEV profiles for a visible brane with large positive cosmological constant are also different from those of the Randall-Sundrum model. We also verify that Goldberger and Wise mechanism can work under nonzero Dirichlet boundary conditions in the generalized Randall-Sundrum model.

scholarly journals The Casimir effect for thick pistons

2016 ◽  
Vol 31 (06) ◽  
pp. 1650012
Author(s):  
Guglielmo Fucci
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Regularization Method ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Numerical Results ◽  
Spectral Zeta Function

In this work, we analyze the Casimir energy and force for a thick piston configuration. This study is performed by utilizing the spectral zeta function regularization method. The results we obtain for the Casimir energy and force depend explicitly on the parameters that describe the general self-adjoint boundary conditions imposed. Numerical results for the Casimir force are provided for specific types of boundary conditions and are also compared to the corresponding force on an infinitely thin piston.

scholarly journals CASIMIR EFFECT FOR THE MASSLESS DIRAC FIELD IN TWO-DIMENSIONAL REISSNER–NORDSTRÖM SPACE–TIME

2006 ◽  
Vol 15 (09) ◽  
pp. 1473-1486 ◽  
Author(s):  
XIN-QIN GAO ◽  
JIAN-YANG ZHU
Keyword(s):  
Black Hole ◽  
Stress Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Space Time ◽  
Dirac Field ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Expectation Values ◽  
Particle Current

In this paper, the two-dimensional Reissner–Nordström black hole is considered as a system of the Casimir type. In this background, the Casimir effect for the massless Dirac field is discussed. The massless Dirac field is confined between two "parallel plates" separated by a distance L and there is no particle current drilling through the boundaries. The vacuum expectation values of the stress tensor of the massless Dirac field at infinity are calculated separately in the Boulware state, the Hartle–Hawking state and the Unruh state.

scholarly journals $T\bar T$ and the mirage of a bulk cutoff

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Monica Guica ◽  
Ruben Monten
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Stress Tensor ◽  
Deformation Parameter ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Gravitational Theory ◽  
Dirichlet Boundary Conditions ◽  
Bulk Solution ◽  
Matter Fields

We use the variational principle approach to derive the large NN holographic dictionary for two-dimen-sional T\bar TTT‾-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial ``bulk cutoff’’ is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.

scholarly journals Casimir Energy in a Bounded Gross-Neveu model

2018 ◽  
Vol 64 (6) ◽  
pp. 577
Author(s):  
Juan Cristóbal Rojas
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Casimir Effect ◽  
Beta Function ◽  
Spatial Dimension ◽  
Casimir Energy ◽  
The Other ◽  
Effective Theory ◽  
Different Boundary Conditions ◽  
Complex Picture

In this letter, we study some relevant parameters of the massless Gross-Neveu (GN) model in afinite spatial dimension for different boundary conditions. It is considered the standard homogeneousHartree-Fock solution using zeta function regularization for the study the mass dynamically generated and its respective beta function. It is found that the beta function does not depend on the boundary conditions. On the other hand, it was considered the Casimir effect of the resulting effective theory. There appears a complex picture where the sign of the generated forces depends on the parameters used in the study.

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