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

Journal Article · Mon Feb 01 04:00:00 EST 1982 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(82)90186-5· OSTI ID:5524541

Nieh, H T; Yan, M L

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.

• Research Organization: Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794
• OSTI ID: 5524541
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 138:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FUNCTIONS
GAUGE INVARIANCE
GREEN FUNCTION
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
RIEMANN SPACE
SPACE
SPINORS
SYMMETRY
WAVE EQUATIONS