Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-01-15
Phys.Rev. D58 (1998) 044002
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, LaTeX, 25 figures
Scientific paper
10.1103/PhysRevD.58.044002
A simple, often invoked, regularization scheme of quantum mechanical path integrals in curved space is mode regularization: one expands fields into a Fourier series, performs calculations with only the first $M$ modes, and at the end takes the limit $M \to \infty$. This simple scheme does not manifestly preserve reparametrization invariance of the target manifold: particular noncovariant terms of order $\hbar^2$ must be added to the action in order to maintain general coordinate invariance. Regularization by time slicing requires a different set of terms of order $\hbar^2$ which can be derived from Weyl ordering of the Hamiltonian. With these counterterms both schemes give the same answers to all orders of loops. As a check we perform the three-loop calculation of the trace anomaly in four dimensions in both schemes. We also present a diagrammatic proof of Matthews' theorem that phase space and configuration space path integrals are equal.
Bastianelli Fiorenzo
Schalm Koenraad
van Nieuwenhuizen Peter
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