The creation of kappa deformed electromagnetic radiation from a sum of zero modes

TL;DR

This paper calculates the creation rate of kappa-deformed electromagnetic radiation between plates, showing it originates from zero mode sums and aligns with previous results, highlighting the effects of deformation and boundary conditions.

Contribution

It introduces a method to compute the radiation creation rate in kappa-deformed electromagnetic fields using zero mode sums and complex analysis techniques.

Findings

The creation rate vanishes when deformation disappears or plates are infinitely separated.

The imaginary part of the effective action relates to zero mode sums.

Results agree with previous findings and clarify the origin of radiation creation.

Abstract

In a related paper we have obtained that the effective action for a kappa-deformed quantum field theory has a real and an imaginary part. The real part is half the sum of the kappa-deformed zero mode frequencies, while the imaginary part is proportional to the sum of the squares of the zero mode frequencies, being proportional to the inverse of kappa. Here we calculate this imaginary part for the kappa-deformed electromagnetic field confined between two perfectly conducting parallel plates. After renormalization this imaginary part gives a creation rate of kappa-deformed electromagnetic radiation. This creation rate goes to zero at the appropriate limits, namely: when the deformation disappears or at infinite separation of the plates. The result agrees with previously obtained results and shed light on them by exhibiting the creation rate as originated in a sum of zero modes. Let us note that due to the rather complicated kappa-deformed electromagnetic dispersion relation we were led to the theorem of the argument in order to sum the squares of the kappa-deformed frequencies.