Quantization of electromagnetic field in the Schwarzschild spacetime

Abstract

We discuss the problem of canonical quantization of electromagnetic field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the internal region of the black hole. We prove that there exists a unitary gauge, which can be viewed as a combination of the Coulomb and Poincare gauges and is compatible with the field equations. The solutions corresponding to the stationary one-particle states of the electromagnetic field are studied, the canonical commutation relations and the Hamiltonian of the quantized electromagnetic field are obtained.

Figures (2)

• Figure 1: Potential $V_{j}(z)$
• Figure 2: $V_{l}(z)$ for $l=0$ (left plot) and $l=1$ (right plot)