A direct approach to the electromagnetic Casimir energy in a rectangular waveguide

Abstract

In this paper we compute the leading order Casimir energy for the electromagnetic field (EM) in an open ended perfectly conducting rectangular waveguide in three spatial dimensions by a direct approach. For this purpose we first obtain the second quantized expression for the EM field with boundary conditions which would be appropriate for a waveguide. We then obtain the Casimir energy by two different procedures. Our main approach does not contain any analytic continuation techniques. The second approach involves the routine zeta function regularization along with some analytic continuation techniques. Our two approaches yield identical results. This energy has been calculated previously for the EM field in a rectangular waveguide using an indirect approach invoking analogies between EM fields and massless scalar fields, and using complicated analytic continuation techniques, and the results are identical to ours. We have also calculated the pressures on different sides and the total Casimir energy per unit length, and plotted these quantities as a function of the cross-sectional dimensions of the waveguide. We also present a physical discussion about the rather peculiar effect of the change in the sign of the pressures as a function of the shape of the cross-sectional area.

The Dirichlet Casimir energy for ϕ 4 theory in a rectangular waveguide

“…The calculation presented in Appendix C proves that the outer waveguides and their remaining boundaries do not affect the Casimir energy of the original waveguide (Region A1). It should be noted that a similar proof to this one was made previously for calculating the electromagnetic Casimir energy inside a conducting rectangular waveguide and the same results were obtained (see Appendix B in [31]). In this study, by applying the second sets of configurations shown in Fig. (2) and the mentioned renormalization program, the zero-and first-order radiative corrections were computed on the Casimir energy for the massive scalar field in φ 4 theory with Dirichlet boundary condition in an open-ended rectangular waveguide.…”

Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach

“…This method was first used by T.H. Boyer for the calculation of the Casimir energy for an electromagnetic field confined in a 3D conducting sphere [26] and it was named Box Subtraction Scheme (BSS) in the later works [27,28]. Up to now, in order to reduce possible ambiguities appearing in the calculation of the Casimir energy, multiple studies used this method [29,30].…”

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

“…Later, in order to reduce the ambiguities in the removal of divergences, this method was remarkably used in other studies [50][51][52]. This technique was also performed to calculate the first order radiative correction to the Casimir energy between two parallel plates for massive scalar field in φ 4 theory in one, two and three spatial dimensions [20,23].…”