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

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.