Canonical quantization of a particle near a black hole

TL;DR

This paper explores the quantization of a particle near an extremal Reissner-Nordstrom black hole, showing how a Hamiltonian redefinition resolves issues with the ground state by interpreting it as a gauge choice.

Contribution

It demonstrates that the DFF Hamiltonian redefinition corresponds to a gauge choice in the quantization of particles near black holes, clarifying the role of boundary obstructions.

Findings

The original Hamiltonian lacks a well-defined ground state.

The DFF redefinition is equivalent to a gauge fixing.

Standard quantization rules are recovered in a suitable gauge.

Abstract

We discuss the quantization of a particle near an extreme Reissner-Nordstrom black hole in the canonical formalism. This model appears to be described by a Hamiltonian with no well-defined ground state. This problem can be circumvented by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF). We show that the Hamiltonian with no ground state corresponds to a gauge in which there is an obstruction at the boundary of spacetime requiring a modification of the quantization rules. The redefinition of the Hamiltonian a la DFF corresponds to a different choice of gauge. The latter is a good gauge leading to standard quantization rules. Thus, the DFF trick is a consequence of a standard gauge-fixing procedure in the case of black hole scattering.