Daubechies, Ingrid; Klauder, John R.; Paul, Thierry Wiener measures for path integrals with affine kinematic variables. (English) Zbl 0615.58008 J. Math. Phys. 28, 85-102 (1987). 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 \(x=0\). Cited in 17 Documents 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 Keywords:path integral; affine coherent state matrix element; unitary evolution operator; Wiener integral × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] DOI: 10.1063/1.1664833 · Zbl 0184.54601 · doi:10.1063/1.1664833 [2] DOI: 10.1063/1.526072 · doi:10.1063/1.526072 [3] DOI: 10.1063/1.526803 · Zbl 0979.81517 · doi:10.1063/1.526803 [4] DOI: 10.1063/1.526761 · Zbl 0571.22021 · doi:10.1063/1.526761 [5] DOI: 10.1063/1.526761 · Zbl 0571.22021 · doi:10.1063/1.526761 [6] DOI: 10.1063/1.526761 · Zbl 0571.22021 · doi:10.1063/1.526761 [7] DOI: 10.1063/1.1704817 · Zbl 0139.45903 · doi:10.1063/1.1704817 [8] DOI: 10.1063/1.1704817 · Zbl 0139.45903 · doi:10.1063/1.1704817 [9] DOI: 10.1063/1.1704817 · Zbl 0139.45903 · doi:10.1063/1.1704817 [10] DOI: 10.1063/1.1704817 · Zbl 0139.45903 · doi:10.1063/1.1704817 [11] DOI: 10.1002/cpa.3160140303 · Zbl 0107.09102 · doi:10.1002/cpa.3160140303 [12] DOI: 10.1090/S0002-9947-1950-0051437-7 · doi:10.1090/S0002-9947-1950-0051437-7 [13] DOI: 10.1063/1.1703636 · Zbl 0092.45105 · doi:10.1063/1.1703636 [14] DOI: 10.1063/1.1703636 · Zbl 0092.45105 · doi:10.1063/1.1703636 [15] DOI: 10.1103/PhysRev.34.57 · JFM 55.0539.02 · doi:10.1103/PhysRev.34.57 [16] DOI: 10.1090/S0002-9904-1976-14149-3 · Zbl 0329.35018 · doi:10.1090/S0002-9904-1976-14149-3 [17] DOI: 10.1090/S0002-9904-1976-14149-3 · Zbl 0329.35018 · doi:10.1090/S0002-9904-1976-14149-3 [18] DOI: 10.1007/BF01609397 · Zbl 1272.53082 · doi:10.1007/BF01609397 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.