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 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 Effects of Quantum Fields Outside Cosmic Strings

1988 ◽  
Vol 130 ◽  
pp. 565-565
Author(s):  
D. A. Konkowski ◽  
T. M. Helliwell
Keyword(s):  
Cosmic String ◽  
Casimir Effect ◽  
Semiclassical Approximation ◽  
Mass Density ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Energy Tensor ◽  
Parallel Plates ◽  
Vacuum Fluctuations ◽  
Gravitational Influence

The space surrounding a long straight cosmic string is flat but conical. The conical topology implies that such a string focuses light rays or particles passing by opposite sides of the string, which can have important astrophysical effects. The flatness, however, implies that the string has no gravitational influence on matter at rest with respect to the string. The flatness is a consequence of the fact that the tension along a cosmic string is equal to its linear mass density μ. There may be physical effects, however, which destroy the equality of tension and mass density, so that straight strings might after all affect matter at rest. One such effect we and others have calculated is the vacuum fluctuations of fields near the strings induced by the conical topology. Such fluctuation s are physically observable but normally small, as in the Casimir effect between parallel plates. We find the vacuum expectation value of the stress - energy tensor of a conformally coupled scalar field around a cosmic string to be in cylindrical coordinates (t, r, θ, z). The equality of Ttt and Tzz means that the effective tension and mass density of the vacuum fluctuations are equal, so that at least in a semiclassical approximation a string dressed by such fields still has no gravitational influence on matter at rest, even though it has a substantial mass density.

scholarly journals Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential

2015 ◽  
Vol 30 (35) ◽  
pp. 1550213 ◽  
Author(s):  
Davide Fermi ◽  
Livio Pizzocchero
Keyword(s):  
Scalar Field ◽  
General Framework ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Harmonic Potential ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Expectation Value ◽  
Stress Energy

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we renormalize the vacuum expectation value of the stress-energy tensor (and of the total energy) for a scalar field in presence of an external harmonic potential.

scholarly journals Analytical Green’s functions for continuum spectra

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Eugenio Megías ◽  
Mariano Quirós
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Dirichlet Boundary ◽  
Green’S Functions ◽  
Neumann Boundary ◽  
Approximate Equation ◽  
New Physics ◽  
Dirichlet Boundary Conditions ◽  
Gauge Bosons ◽  
Linear Dilaton

Abstract Green’s functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension z, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS5, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to z → ∞. This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green’s functions (with a mass gap mg ∼ TeV and a continuum for s >$$ {m}_g^2 $$ m g 2 ) which could then be easily incorporated in the experimental codes. The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. All Green’s functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at s = $$ {M}_n^2 $$ M n 2 − iMnΓn, denoting a discrete (infinite) set of broad resonances with masses (Mn) and widths (Γn). For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation s = −4$$ {m}_g^2{\mathcal{W}}_n^2 $$ m g 2 W n 2 [±(1 + i)/4], where $$ \mathcal{W} $$ W n is the n-th branch of the Lambert function.

scholarly journals Vacuum expectation values in nontrivial background space from three types of UV improved Green’s functions

2021 ◽  
Vol 36 (01) ◽  
pp. 2150001
Author(s):  
Nahomi Kan ◽  
Masashi Kuniyasu ◽  
Kiyoshi Shiraishi ◽  
Zhenyuan Wu
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Vacuum Expectation ◽  
Expectation Values ◽  
Background Space ◽  
Connected Spaces

We evaluate the quantum expectation values in nonsimply connected spaces by using UV improved Green’s functions proposed by Padmanabhan, Abel, and Siegel. It is found that the results from these three types of Green’s functions behave similarly under changes of scales, but have minute differences. Prospects in further applications are briefly discussed.

scholarly journals Analysis of scalar and fermion quantum field theory on anti-de Sitter spacetime

2018 ◽  
Vol 27 (11) ◽  
pp. 1843014 ◽  
Author(s):  
Victor E. Ambruş ◽  
Carl Kent ◽  
Elizabeth Winstanley
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Vacuum Expectation ◽  
Dirac Fermion ◽  
De Sitter ◽  
Expectation Values ◽  
Sitter Spacetime ◽  
Fermion Fields ◽  
Spacetime Curvature ◽  
Ads Spacetime

We study vacuum and thermal expectation values of quantum scalar and Dirac fermion fields on anti-de Sitter (adS) spacetime. AdS spacetime is maximally symmetric and this enables expressions for the scalar and fermion vacuum Feynman Green’s functions to be derived in closed form. We employ Hadamard renormalization to find the vacuum expectation values (v.e.v.s). The thermal Feynman Green’s functions are constructed from the vacuum Feynman Green’s functions using the imaginary time periodicity/anti-periodicity property for scalars/fermions. Focusing on massless fields with either conformal or minimal coupling to the spacetime curvature (these two cases being the same for fermions) we compute the differences between the thermal expectation values and v.e.v.s. We compare the resulting energy densities, pressures and pressure deviators with the corresponding classical quantities calculated using relativistic kinetic theory.

On seismic deghosting using integral representation for the wave equation: Use of Green’s functions with Neumann or Dirichlet boundary conditions

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T89-T98 ◽  
Author(s):  
Lasse Amundsen ◽  
Arthur B. Weglein ◽  
Arne Reitan
Keyword(s):  
Wave Equation ◽  
Integral Representation ◽  
Boundary Conditions ◽  
Representation Theorem ◽  
Green's Functions ◽  
Dirichlet Boundary ◽  
Green’S Functions ◽  
Dirichlet Boundary Conditions ◽  
Sea Surface ◽  
Receiver Side

The recent interest in broadband seismic technology has spurred research into new and improved seismic deghosting solutions. One starting point for deriving deghosting methods is the representation theorem, which is an integral representation for the wave equation. Recent research results show that by using Green’s functions with Dirichlet boundary conditions in the representation theorem, source-side deghosting of already receiver-side deghosted wavefields can be achieved. We found that the choice of Green’s functions with Neumann boundary conditions on the sea surface and the plane that contains the sources leads to an identical but simpler solution with fewer processing steps. In addition, we found that pressure data can be receiver-side deghosted by introducing Green’s functions with Dirichlet boundary conditions on the sea surface and the plane containing the receivers into a modified representation theorem. The deghosting methods derived from the representation theorem are wave-theoretic algorithms defined in the frequency-space domain and can accommodate streamers of any shape (e.g., slanted). Our theoretical analysis of deghosting is performed in the frequency-wavenumber domain where analytical deghosting solutions are well known and thus are available for verifying the solutions. A simple numerical example can be used to show how source-side deghosting can be performed in the space domain by convolving data with Green’s functions.

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