scholarly journals Casimir effect with one large extra dimension

2021 ◽  
Author(s):  
Andrea Erdas
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Extra Dimension ◽  
Casimir Effect ◽  
Neumann Boundary ◽  
Casimir Energy ◽  
Neumann Boundary Conditions ◽  
Three Dimensions ◽  
Parallel Plates ◽  
Large Extra Dimension

In this work, I study the Casimir effect of a massive complex scalar field in the presence of one large compactified extra dimension. I investigate the case of a scalar field confined between two parallel plates in the macroscopic three dimensions, and examine the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on the plates. The case of Neumann boundary conditions is uninteresting, since it yields the same result as the case of Dirichlet boundary conditions. The scalar field also permeates a fourth compactified dimension of a size that could be comparable to the distance between the plates. This investigation is carried out using the [Formula: see text]-function regularization technique that allows me to obtain exact expressions for the Casimir energy and pressure. I discover that when the compactified length of the extra dimension is similar to the plate distance, or slightly larger, the Casimir energy and pressure become significantly different than their standard three-dimensional values, for either Dirichlet or mixed boundary conditions. Therefore, the Casimir effect of a quantum field that permeates a compactified fourth dimension could be used as an effective tool to explore the existence of large compactified extra dimensions.

scholarly journals Casimir effect of a Lorentz-violating scalar in magnetic field

2020 ◽  
Vol 35 (31) ◽  
pp. 2050209
Author(s):  
Andrea Erdas
Keyword(s):  
Magnetic Field ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Effect ◽  
Lorentz Invariance ◽  
Neumann Boundary ◽  
Casimir Energy ◽  
Neumann Boundary Conditions ◽  
Parallel Plates ◽  
Massive Scalar Field

In this paper, I study the Casimir effect caused by a charged and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. I investigate the case of a scalar field that satisfies Dirichlet or mixed (Dirichlet–Neumann) boundary conditions on a pair of very large plane parallel plates. The case of Neumann boundary conditions is straightforward and will not be examined in detail. I use the [Formula: see text]-function regularization technique to study the effect of a constant magnetic field, orthogonal to the plates, on the Casimir energy and pressure. I investigate the cases of a timelike Lorentz asymmetry, a spacelike Lorentz asymmetry in the direction perpendicular to the plates, and a spacelike asymmetry in the plane of the plates and, in all those cases, derive simple analytic expressions for the zeta function, Casimir energy and pressure in the limits of small plate distance, strong magnetic field and large scalar field mass. I discover that the Casimir energy and pressure, and their magnetic corrections, all strongly depend on the direction of the unit vector that implements the breaking of the Lorentz symmetry.

scholarly journals Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field

2021 ◽  
pp. 2150155
Author(s):  
Andrea Erdas
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Lorentz Invariance ◽  
Main Tool ◽  
Neumann Boundary ◽  
Casimir Energy ◽  
Neumann Boundary Conditions ◽  
Function Technique ◽  
Parallel Plates ◽  
The Magnetic Field

In this work, I investigate the finite temperature Casimir effect due to a massive and charged scalar field that breaks Lorentz invariance in a CPT-even, aether-like way. I study the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on a pair of parallel plates. I will not examine the case of Neumann boundary conditions since it produces the same results as Dirichlet boundary conditions. The main tool used in this investigation is the [Formula: see text]-function technique that allows me to obtain the Helmholtz free energy and Casimir pressure in the presence of a uniform magnetic field perpendicular to the plates. Three cases of Lorentz asymmetry are studied: timelike, spacelike and perpendicular to the magnetic field, spacelike and parallel to the magnetic field. Asymptotic cases of small plate distance, high temperature, strong magnetic field, and large mass will be considered for each of the three types of Lorentz asymmetry and each of the two types of boundary conditions examined. In all these cases, simple and very accurate analytic expressions of the thermal corrections to the Casimir energy and pressure are obtained and I discover that these corrections strongly depend on the direction of the unit vector that produces the breaking of the Lorentz symmetry.

Electromagnetic thermal corrections to Casimir energy

2016 ◽  
Vol 31 (22) ◽  
pp. 1650127 ◽  
Author(s):  
Borzoo Nazari
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Scalar Field ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Parallel Plates ◽  
Weak Gravitational Field

In [B. Nazari, Mod. Phys. Lett. A 31, 1650007 (2016)], we calculated finite temperature corrections to the energy of the Casimir effect of two conducting parallel plates in a general weak gravitational field. The calculations was done for the case a scalar field was present between the plates. Here we find the same results in the presence of an electromagnetic field.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC SPHERES

2012 ◽  
Vol 27 (16) ◽  
pp. 1250082 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Outer Radius ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
New Approach ◽  
Concentric Spheres ◽  
Spherical Boundary

The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We developed a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, ([Formula: see text] where a(b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.

ON THE EFFECTS OF THE NEUMANN BOUNDARY CONDITIONS IN THE COLEMAN–WEINBERG MECHANISM

2010 ◽  
Vol 25 (07) ◽  
pp. 1389-1403 ◽  
Author(s):  
F. N. FAGUNDES ◽  
T. L. ANTONACCI OAKES ◽  
B. B. DILEM ◽  
J. A. NOGUEIRA
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Symmetry Breaking ◽  
Boundary Conditions ◽  
Spontaneous Symmetry Breaking ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Finite Region

We investigate the effects of the homogeneous Neumann boundary conditions in the scalar electrodynamics with self-interaction. We show that if the length of the finite region is small enough ([Formula: see text], where Mϕ is the mass of the scalar field generated by the Coleman–Weinberg mechanism) the spontaneous symmetry breaking will not be induced and the vector field will not develop mass, however the scalar field will.

scholarly journals Casimir effect in Horava–Lifshitz-like theories

2015 ◽  
Vol 30 (36) ◽  
pp. 1550220 ◽  
Author(s):  
I. J. Morales Ulion ◽  
E. R. Bezerra de Mello ◽  
A. Yu. Petrov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Scalar Field Theory

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.

scholarly journals CASIMIR ENERGY DENSITY IN CLOSED HYPERBOLIC UNIVERSES

2002 ◽  
Vol 17 (29) ◽  
pp. 4385-4392 ◽  
Author(s):  
DANIEL MÜLLER ◽  
HELIO V. FAGUNDES
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Energy Density ◽  
Boundary Conditions ◽  
Negative Curvature ◽  
Casimir Effect ◽  
Casimir Energy ◽  
The Difference

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

scholarly journals Eigenvalues of the Laplacian for rectilinear regions

1988 ◽  
Vol 29 (3) ◽  
pp. 270-281 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Spectral Function ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Three Dimensions ◽  
Eigenvalue Spectrum ◽  
Corner Angle ◽  
Eigenvalues Of The Laplacian ◽  
Extract Information

AbstractFrom a knowledge of the eigenvalue spectrum of the Laplacian on a domain, one may extract information on the geometry and boundary conditions by analysing the asymptotic expansion of a spectral function. Explicit calculations are performed for isosceles right-angle triangles with Dirichlet or Neumann boundary conditions, yielding in particular the corner angle terms. In three dimensions, right prisms are dealt with, including the solid vertex terms.

scholarly journals One-loop correction to the Casimir energy in Lifshitz-like theory

2021 ◽  
pp. 2150204
Author(s):  
M. A. Valuyan
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Perturbation Expansion ◽  
Neumann Boundary ◽  
Mixed Boundary Conditions ◽  
Casimir Energy ◽  
Dependent Manner ◽  
Loop Correction ◽  
Systematic Perturbation

In this paper, Radiative Correction (RC) to the Casimir energy was computed for the self-interacting massive/massless Lifshitz-like scalar field, confined between a pair of plates with Dirichlet and Mixed boundary conditions in 3 + 1 dimensions. Moreover, using the results obtained for the Dirichlet Casimir energy, the RC to the Casimir energy for Periodic and Neumann boundary conditions were also draw outed. To renormalize the bare parameters of the Lagrangian, a systematic perturbation expansion was used in which the counterterms were automatically obtained in a position-dependent manner. In our view, the position dependency of the counterterm was allowed, since it reflected the effects of the boundary condition imposed or the background space in the problem. All the answers obtained for the Casimir energy were consistent with well-known physical expects. In a language of graphs, the Casimir energy for the massive Lifshitz-like scalar field confined with four boundary conditions (Dirichlet, Neumann, Mixed, and Periodic) was also compared to each other, and as a concluding remark, the sign and magnitude of their values were discussed.

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