This article is cited in 2 papers

Infrared Asymptotics of the Heat Kernel and Nonlocal Effective Action

A. O. Barvinsky, D. V. Nesterov

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We review recent results in the nonperturbative theory of the heat kernel and its late-time asymptotic properties responsible for the infrared behavior of the quantum effective action for massless theories. In particular, we derive a generalization of the Coleman–Weinberg potential for theories with an inhomogeneous background field. This generalization represents a new nonlocal, nonperturbative action accounting for the effects in a transition domain between the space-time interior and its infinity. In four dimensions, these effects delocalize the logarithmic Coleman-Weinberg potential, while in $d>4$, they are dominated by a new powerlike, renormalization-independent nonlocal structure. We also consider the nonperturbative behavior of the heat kernel in a curved space-time with an asymptotically flat geometry. In particular, we analyze the conformal properties of the heat kernel for a conformally invariant scalar field and discuss the problem of segregating the local cosmological term from the nonlocal effective action.

Keywords: effective action, nonlocal field theories, Schwinger–DeWitt expansion.

Received: 02.11.2004

DOI: 10.4213/tmf1817

 English version: Theoretical and Mathematical Physics, 2005, 143:3, 760–781

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