New look at the Riemann-Cartan theory

Journal Article · Sun Jul 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.464· OSTI ID:7057576

Aurilia, A ^[1]; Spallucci, E ^[2]

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1. Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (USA) Department of Physics, California State Polytechnic University, Pomona, CA (USA)
2. Istituto di Fisica Teorica, Universita di Trieste, Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, 34100 Trieste (Italy)

The geometry of torsion in the Riemann-Cartan (RC) theory can be described by an Abelian axial-vector field interacting with the axial-vector fermion current in a purely Riemannian background. On the basis of this observation we note that the Schwinger model formulated in curved spacetime can be interpreted as the two-dimensional version of the RC theory. In two dimensions as well as in four dimensions there is a one-parameter family of regulators that can be used to compute the axial anomaly. In four dimensions we set the value of the arbitrary parameter equal to zero and compute the axial anomaly, including counterterms, using Fujikawa's approach. The addition of the Wess-Zumino Lagrangian changes the original RC theory into a nonanomalous Abelian gauge theory of the torsion field. Guided by the analogy with the Schwinger model, we offer several forms of {ital L}{sub gravity} from which one can deduce the spin content of the quanta of torsion.

• DOE Contract Number: AC03-76SF00515
• OSTI ID: 7057576
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:2; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRAIC CURRENTS
AXIAL-VECTOR CURRENTS
COSMOLOGICAL MODELS
CURRENTS
FERMIONS
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LORENTZ TRANSFORMATIONS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
QUANTUM FIELD THEORY
RIEMANN SPACE
SPACE
SPACE-TIME
TORSION
TRANSFORMATIONS