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Canonical quantization of a particle near a black hole

George Siopsis
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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.

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George Siopsis. 2000-06-12. Canonical quantization of a particle near a black hole. https://doi.org/10.1103/physrevd.62.104011

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