Revivals and Casimir energy for a free Maxwell field (spin-1 singleton) on R x S^d for odd d

TL;DR

This paper extends the study of quantum revivals and Casimir energy calculations to spin-one Maxwell fields on R x S^d, utilizing Barnes zeta functions and connecting with AdS/CFT results.

Contribution

It introduces new calculations of Casimir energy for Maxwell fields on curved spaces and explores higher order singletons, linking mathematical techniques with theoretical physics.

Findings

Casimir energy expressed as a polynomial in singleton order

Application of Barnes zeta-functions and Bernoulli polynomials

Connections established with AdS/CFT calculations

Abstract

Earlier work on quantum revivals is extended to Maxwell fields (aka spin-one singletons). An evaluation of the Casimir energy on the generalised Einstein universe is also done to illustrate the utility of the Barnes zeta--function and generalised Bernoulli polynomials. Contact is made with some recent calculations in AdS/CFT. In particular. higher order singletons are considered with the Casimir energy being a polynomial in the order.