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Nonlinear Nonlocal Substitutions in Functional Integrals

Abstract

It is shown that nonlinear nonlocal substitutions in functional integrals lead to the need of integration over functional spaces that include functions with singularities. This makes it possible to formulate a quantum theory in cases where singularities are essential, e.g., in quantum cosmology. The proper accounting of singularities in functional integrals gives an additional unexpected effect, which we call “quantum restoration of broken symmetry.”

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Correspondence to V. V. Belokurov or E. T. Shavgulidze.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 5, pp. 47–59, 2016.

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Belokurov, V.V., Shavgulidze, E.T. Nonlinear Nonlocal Substitutions in Functional Integrals. J Math Sci 248, 544–552 (2020). https://doi.org/10.1007/s10958-020-04895-x

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