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Daubechies, Ingrid; Klauder, John R.

Quantum-mechanical path integrals with Wiener measure for all polynomials Hamiltonians. II. (English) Zbl 0979.81517

J. Math. Phys. 26, No. 9, 2239-2256 (1985).
Summary: The coherent-state representation of quantum-mechanical propagators as well-defined phase-space path integrals involving Wiener measure on continuous phase-space paths in the limit that the diffusion constant diverges is formulated and proved. This construction covers a wide class of selfadjoint Hamiltonians, including all those which are polynomials in the Heisenberg operators; in fact, this method also applies to maximal symmetric Hamiltonians that do not possess a selfadjoint extension. This construction also leads to a natural covariance of the path integral under canonical transformations. An entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin-operator Hamiltonian as well-defined path integrals involving Wiener measure on the unit sphere, again in the limit that the diffusion constant diverges.

Cited in 27 Documents

MathOverflow Questions:

Path integral as quantum mechanics on the tangent bundle

MSC:

81S40 Path integrals in quantum mechanics
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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References:

[1] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[2] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[3] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[4] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[5] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[6] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[7] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[8] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[9] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[10] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[11] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[12] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[13] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[14] DOI: 10.1063/1.1704124 · Zbl 0133.22905 · doi:10.1063/1.1704124
[15] Klauder J. R., Phys. Rev. 52 pp 1161– (1984)
[16] DOI: 10.1007/BF02790311 · Zbl 0133.07701 · doi:10.1007/BF02790311
[17] DOI: 10.1007/BF01646493 · Zbl 1125.82305 · doi:10.1007/BF01646493
[18] DOI: 10.1002/cpa.3160140303 · Zbl 0107.09102 · doi:10.1002/cpa.3160140303
[19] DOI: 10.1017/S0305004100000487 · doi:10.1017/S0305004100000487
[20] DOI: 10.1017/S0305004100000487 · doi:10.1017/S0305004100000487
[21] DOI: 10.1063/1.525234 · doi:10.1063/1.525234
[22] DOI: 10.1103/PhysRevB.29.5617 · doi:10.1103/PhysRevB.29.5617
[23] DOI: 10.1007/BF00400438 · Zbl 0521.60078 · doi:10.1007/BF00400438
[24] DOI: 10.1063/1.525233 · doi:10.1063/1.525233
[25] DOI: 10.1016/0022-1236(68)90020-7 · Zbl 0157.21501 · doi:10.1016/0022-1236(68)90020-7
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