A Model of Electrodynamics in the Momentum Space of Constant Curvature

Abstract

We have considered the quantum field theory in the momentum space of constant curvature, [1], [2], [3], [4]. It was shown in these papers that the mass shell of the particle could be embedded in the momentum space of constant curvature. Using this fact the quantum field theory was developed in which exit off the mass shell is made not in the flat Minkowsky p-space but in- the De-Sitter p-space. It was shown in [3] that theory like that does not contain ultraviolet divergencies. The essential role in this approach is played by the universal constant — the fundamental mass M ( or the fundamental length 1, M = ^ħ /lc, further we shall use the the natural unit system in which ħ = c = M = 1).

The gauge transformations consistent with the hypothesis of the curved momentum space are considered. In this case the components of the electromagnetic field are not commuting. The finite-difference analog of the D’Alambert equation is derived.