We suggest a new method for the calculation of the nonlocal part of the effective action. It is based on the resummation of the perturbation series for the heat kernel and its functional trace at large values of the proper time parameter. We derive a new, essentially nonperturbative, nonlocal contribution to the effective action in spacetimes with dimensions $d>2.$
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Barvinsky et al. (2002) studied this question.
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