Canonical analysis of electrodynamics in 5D

We review the canonical analysis of Maxwell's theory in five dimensions (5D). In the first part we summarize the canonical analysis of the free theory in Minkowski space-time. As is well known the theory has two first class constraints and therefore two gauge conditions are needed in order to fix the gauge completely. In particular we discuss the properties of the axial gauge. In the second part we discuss the theory in a different 5D background. We consider a space-time in which the fifth dimension is a circle (Kaluza-Klein dimensional reduction). We show that the axial gauge is not consistent with the periodic boundary conditions in the fifth coordinate. As a consequence it is necessary to introduce a different gauge, the 'almost axial gauge'.