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Dimensional regularization of nonlinear sigma models on a finite time interval. (English) Zbl 1058.81600

Summary: We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (“quantum mechanical path integrals in curved space”) dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by 1/8\(\hslash^2\)R.

MSC:

81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
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