Canonical quantization of gauge fields in static space-times with applications to Rindler spaces

The canonical quantization in the Weyl gauge of gauge fields in static space-times is presented. With an appropriate definition of transverse and longitudinal components of gauge fields, the Gauss law constraint is resolved explicitly for scalar and spinor QED and a complete nonperturbative solution is given for the quantized Maxwell field coupled to external currents. The formalism is applied in investigations of the electromagnetic field in Rindler spaces. The relation of creation and annihilation operators in Minkowski and Rindler spaces is established, and initial value problems associated with bremsstrahlung of a uniformly accelerated charge are studied. The peculiar scaling properties of scalar and gauge theories in Rindler spaces are discussed, and various quantities such as the photon condensate or the interaction energy of static charges and of scalar sources are computed.

Figure 1

The interaction energy (205) (solid lines) for $d=1$, 2, 3 and the small distance approximation (207) (dashed lines) as a function of the geodesic distance $s$. Up to an additive constant the small distance approximation coincides with the interaction energy of static charges in the inertial system. The curves for $d=1$ and $d=2$ are shifted by 0.5