Generally covariant quantization and the Dirac field

Journal Article · Mon Oct 15 00:00:00 EDT 2007 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.04.001· OSTI ID:21077640

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.

• OSTI ID: 21077640
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 10 Vol. 322; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATORS
FIELD THEORIES
HAMILTONIANS
LAGRANGIAN FUNCTION
MOMENTUM TRANSFER
SECOND QUANTIZATION
SPACE-TIME