Cancellation of quantum mechanical higher loop contributions to the gravitational chiral anomaly

Abstract

We give an explicit demonstration, using the rigorous Feynman rules developed in~$\0^{1}$, that the regularized trace $\tr γ_5 e^{-β\Dslash^2}$ for the gravitational chiral anomaly expressed as an appropriate quantum mechanical path integral is $\beta$-independent up to two-loop level. Identities and diagrammatic notations are developed to facilitate rapid evaluation of graphs given by these rules.

10 pages, LaTeX and psfig (many figures)

References in corpus (3)

• Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies
• Loop calculations in quantum-mechanical non-linear sigma models
• Graphical Representation of Invariants and Covariants in General Relativity

Cited by in corpus (4)

• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• BRST treatment of zero modes for the worldline formalism in curved space
• Unique Translation between Hamiltonian Operators and Functional Integrals
• Trace and chiral anomalies in string and ordinary field theory from Feynman diagrams for nonlinear sigma models