New formulation of the anomaly, the anomaly formula, and a graphical representation

Journal Article · Wed May 01 04:00:00 EDT 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.5932· OSTI ID:284031

Ichinose, S; Ikeda, N ^[1]

---

1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01 (Japan)

A general approach to the anomaly in quantum field theory is formulated by using the propagator theory in solving the heat-kernel equation. We regard the heat kernel as a sort of point-splitting regularization in the space(-time) manifold. Fujikawa{close_quote}s general standpoint that the anomalies come from the path-integral measure is taken. We obtain some useful formulas which are valid for general anomaly calculations. They turn out to be the same as the one-loop counterterm formulas except some important total derivative terms. Various anomalies in two- and four-dimensional theories are systematically calculated. Some important relations between them are concretely shown. As for the representation of general [global SO({ital n})] tensors, we introduce a graphical one. It makes the tensor structure of invariants very transparent and makes the tensor calculation so simple. {copyright} {ital 1996 American Institute of Physics}

• OSTI ID: 284031
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 10 Vol. 53; ISSN 0556-2821; ISSN PRVDAQ
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANOMALOUS PROPERTIES
FEYNMAN PATH INTEGRAL
FOUR-DIMENSIONAL CALCULATIONS
KERNELS
PROPAGATOR
QUANTUM FIELD THEORY
SO GROUPS
SPACE-TIME
TENSORS
TWO-DIMENSIONAL CALCULATIONS