Generally covariant quantization and the Dirac field

Details Generally covariant quantization and the Dirac field Generally covariant quantization and the Dirac field

2006-06-08

arxiv.org/abs/gr-qc/0606033v4

AnnalsPhys.322:2279-2303,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

final version, to appear in Annals Phys

Scientific paper

10.1016/j.aop.2007.04.001

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.

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