| Abstract: | The Feynman measure is defined as a linear continuous functional on a test-function space (introduced in the paper). 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—Maruyama, 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.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 1, pp. 3–13, July, 1994. |
