Casimir energy in the Fulling--Rindler vacuum

TL;DR

This paper calculates the Casimir energy for various quantum fields in the Fulling--Rindler vacuum with parallel plates undergoing uniform acceleration, revealing finite energies and interference effects in different dimensions.

Contribution

It provides a comprehensive analysis of Casimir energies in accelerated frames using zeta function techniques, including new results for single and double plate configurations in arbitrary dimensions.

Findings

Casimir energies are finite in odd spatial dimensions when considering the whole Rindler wedge.

The total Casimir energy can be positive or negative depending on the field type and boundary conditions.

Interference terms between plates are negative for all separations and field types.

Abstract

The Casimir energy is evaluated for massless scalar fields under Dirichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by uniform proper acceleration through the Fulling--Rindler vacuum in an arbitrary number of spacetime dimension. For the geometry of a single plate the both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are considered. The zeta function technique is used, in combination with contour integral representations. The Casimir energies for separate RR and RL regions contain pole and finite contributions. For an infinitely thin plate taking RR and RL regions together, in odd spatial dimensions the pole parts cancel and the Casimir energy for the whole Rindler wedge is finite. In $d=3$ spatial dimensions the total Casimir energy for a single plate is negative for Dirichlet scalar and positive for Neumann scalar and the electromagnetic field. The total Casimir energy for two plates geometry is presented in the form of a sum of the Casimir energies for separate plates plus an additional interference term. The latter is negative for all values of the plates separation for both Dirichlet and Neumann scalars, and for the electromagnetic field.