ar X iv : h ep - t h / 03 05 15 8 v 1 1 9 M ay 2 00 3 The creation of kappa deformed electromagnetic radiation from a sum of zero modes

In a related paper we have obtained that the effective action for a κ-deformed quantum field theory has a real and an imaginary part. The real part is half the sum of the κ-deformed zero mode frequencies, while the imaginary part is proportional to the sum of the squares of the zero mode frequencies, being the proportionality constant equal to the inverse of 2πκ. Here we calculate this imaginary part for the κ-deformed electromagnetic field confined between two perfectly conducting parallel plates. After renormalization this imaginary part gives a creation rate of κ-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 κ-deformed electromagnetic dispersion relation we were led to the theorem of the argument in order to sum the squares of the κ-deformed frequencies. In a companion [1] paper, we have obtained that the effective action of a κ-deformed field theory [2] has a real part that is the usual sum of frequencies of zero modes and an imaginary part given by a sum of the squares of these frequencies. For the electromagnetic field this imaginary part is given in terms of the parameter q = (2κ) as: I { W T }