Dirac quantum fields in curved space-time

Details Dirac quantum fields in curved space-time Dirac quantum fields in curved space-time

Aug 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt.........2j&link_type=abstract

Thesis (PhD). STATE UNIVERSITY OF NEW YORK AT BUFFALO, Source DAI-B 60/02, p. 682, Aug 1999, 77 pages.

Mathematics

1

Scientific paper

It is our interest to investigate Dirac fields under gravitational background. Conventionally, in curved space-time the Dirac spinor fields are generalized using vierbein (tetrad) fields so that the Dirac field equation can be constructed invariantly under both local Lorentz and global curved space-time transformations. With a general relativistic equation of Dirac fields on Schwarzschild metric, we develop a classical scattering theory for massive Dirac fields. The existence of modified wave operators at infinity is shown by implementing a time-dependent logarithmic phase shift from the free dynamics to offset a long-range mass term. To study the quantum theory of Dirac fields, we consider only static space-time with time-independent metric. We can make Fourier transformation along time direction and also separate the positive and negative energy fields. Moreover, we can show that the time component of spin affine connection of Dirac fields vanishes. This helps us to find the propagator of Dirac equation explicitly. With rigorous mathematical deduction, we prove that the Dirac field operators in static space-time can be quantized in terms of the creation and annihilation operators on Fermi-Fock space by using two continuous projections onto the positive and negative energy subspaces. The time evolution of Dirac fields and anti-particle picture are discussed at the end.

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