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

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.

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

International Journal of Modern Physics D ◽

10.1142/s0218271818430149 ◽

2018 ◽

Vol 27 (11) ◽

pp. 1843014 ◽

Cited By ~ 3

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x21501682 ◽

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.

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