Publications [#287125] of Ingrid Daubechies

Papers Published

1. Daubechies, I; Klauder, JR, Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II, Journal of Mathematical Physics, vol. 26 no. 9 (January, 1985), pp. 2239-2256, AIP Publishing, ISSN 0022-2488 [doi]
   (last updated on 2024/04/23)

   Abstract:
   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 self-adjoint 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 self-adjoint 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. © 1985 American Institute of Physics.