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Transformations of Feynman integrals under nonlinear transformations of the phase space. (English. Russian original) Zbl 1041.81549
Theor. Math. Phys. 100, No. 1, 803-810 (1994); translation from Teor. Mat. Fiz. 100, No. 1, 3-13 (1994).
Summary: The Feynman measure is defined as a linear continuous functional on a test-function space. The functional is given by means of its Fourier transform. Not only a positive-definite correlation operator but also one without fixed sign is considered (the latter case corresponds to the so-called symplectic, or Hamiltonian, Feynman measure). The Feynman integral is the value of the Feynman measure on a function (in the test-function space). The effect on the Feynman measure of nonlinear transformations of the phase space in the form of shifts along vector fields or along integral curves of vector fields is described. Analogs of the well-known Cameron-Martin, Girsanov-Martyama, and Ramer formulas in the theory of Gaussian measures are obtained. The results of the paper can be regarded as formulas for a change of variable in Feynman integrals.

MSC:
81S40 Path integrals in quantum mechanics
46F25 Distributions on infinite-dimensional spaces
46G12 Measures and integration on abstract linear spaces
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