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Wiener measures for path integrals with affine kinematic variables. (English) Zbl 0615.58008
The results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp(-iTH) can be written as a well-defined Wiener integral, involving Wiener measure on the Lobachevsky half-plane, in the limit that the diffusion constant diverges. This approach works for a wide class of Hamiltonians, including, e.g., \(-d^ 2/dx^ 2+V(x)\) on \(L^ 2({\mathbb{R}}_+)\), with V sufficiently singular at \(x=0\).

MSC:
58D30 Applications of manifolds of mappings to the sciences
81S40 Path integrals in quantum mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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