Trace anomalies and the string-inspired definition of quantum-mechanical path integrals in curved space

Abstract

We consider quantum-mechanical path integrals for non-linear sigma models on a circle defined by the string-inspired method of Strassler, where one considers periodic quantum fluctuations about a center-of-mass coordinate. In this approach one finds incorrect answers for the local trace anomalies of the corresponding $n$-dimensional field theories in curved space. The quantum field theory approach to the quantum-mechanical path-integral, where quantum fluctuations are not periodic but vanish at the endpoints, yields the correct answers. We explain these results by a detailed analysis of general coordinate invariance in both methods. Both approaches can be derived from the same operator expression and the integrated trace anomalies in both schemes agree. In the string-inspired method the integrands are not invariant under general coordinate transformations and one is therefore not permitted to use Riemann normal coordinates.

LaTeX, 12 pages, 17 figures

References in corpus (2)

• Mode regularization, time slicing, Weyl ordering and phase space path integrals for quantum mechanical nonlinear sigma models
• Trace and chiral anomalies in string and ordinary field theory from Feynman diagrams for nonlinear sigma models

Cited by in corpus (10)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Worldline formalism in a gravitational background
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• Gravitational corrections to the Euler-Heisenberg Lagrangian
• BRST treatment of zero modes for the worldline formalism in curved space
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Dimensional regularization of nonlinear sigma models on a finite time interval
• Dimensional regularization of the path integral in curved space on an infinite time interval
• Integrals over Products of Distributions from Manifest Coordinate Invariance of Perturbation Expansions of Path Integrals in Curved Space
• Worldline approach to the Grosse-Wulkenhaar model