Casimir effect in kappa deformed electrodynamics

Abstract

We consider the quantization of a scalar κ-deformed field up to the point of obtaining an expression for its vacuum energy. The expression is given by the half sum of the field frequencies, as in the nondeformed case, but with the frequencies obeying the κ-deformed dispersion relation. We consider a set of κ-deformed Maxwell equations and show that for the purpose of calculating the Casimir energy the Maxwell field, as in the non-deformed case, behaves as a pair of scalar fields. Those results provide a foundation for computing the Casimir energy starting from the the half sum of field frequencies. A method of calculation starting from this expression is briefly described.

Time-space noncommutativity and Casimir effect

“…Note that we have obtained the corrections to Casimir energy that scale as L −5 in addition to terms that scale as L −3 . This should be contrasted with the result of [37], where the correction was scaling as L −3 , only.…”

“…Thus definition of conjugate momentum is not straight forward as in the commutative theory. In the approach used in [37], the conjugate momentum used is not unique. The issue is addressed by calculating the expression for energy corresponding to the scalar theory without using explicit form of conjugate momentum.…”

“…Using this, Casimir energy is calculated where the boundary conditions imposed are same as the ones in commutative space-time. Casimir energy is shown to scale as L −3 in this case [37]. For 1 + 1 dimension, in commutative case, Casimir effect for two parallel plates, has been rederived by considering two δ-function potentials [38], which imply that the parallel plates are at x = 0 and x = L, respectively.…”

“…Many results in this direction have been reported in recent times. Effects of minimal length, GUP and modified dispersion relations on Casimir force and corresponding energy have been investigated by various authors [29,30,31,32,33,34,35,36,37].Generalised commutation relations between coordinates and momenta as well as those between coordinates among themselves have been studied in the context of quantum gravity and they are known to be related to generalised uncertainty relations and minimal length scale. These coordinates are realised in terms of usual coordinates, momenta and parameter(s) characterising the modified commutation relations.…”

Analytical regularization for confined quantum fields between parallel surfaces

“…These theories which may be important in some models of the early universe lead in general to highly nontrivial dispersion relations. See [12] and references therein. Consider for example scalar κ-deformed electrodynamics.…”