Quantized Dirac field in curved Riemann-Cartan background. I. Symmetry properties, Green's function

Abstract

In the present series of papers, we study the properties of quantized Dirac field in curved Riemann-Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann-Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann-Cartan background, using the Schwinger-DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background.