Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Reports on Mathematical Physics

Construction of quantum-mechanical dynamics by means of path integrals in phase space

Krzysztof Gawędzki

Published Dec 1, 1974• 9 citations
Publisher
DOI
10.1016/s0034-4877(74)80002-9

Related papers

Coherent States in Action

John R. Klauder

Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the variables involved that is manifestly inconsistent. On the other hand, a phase space path integral based on coherent states entails variables that exhibit a self-consistent physical meaning.

arXiv:quant-ph/9710029•Oct 8, 1997•5 citations

Path Integrals in Quantum Mechanics

WORLD SCIENTIFIC eBooks•Feb 1, 1996•60 citations

Path Integrals in Quantum Mechanics

Rainer Dick

Graduate texts in physics•Jan 1, 2020•14 citations

Constructing measures for path integrals

Ingrid C. Daubechies, John R. Klauder

The overcompleteness of the coherent states for the Heisenberg–Weyl group implies that many different integral kernels can be used to represent the same operator. Within such an equivalence class we construct an integral kernel to represent the quantum-mechanical evolution operator for certain dynamical systems in the form of a path integral that involves genuine (Wiener) measures on continuous phase-space paths. To achieve this goal it is necessary to employ an expression for the classical action different from the usual one.

Journal of Mathematical Physics•Oct 1, 1982•15 citations

Path Integrals in Quantum Mechanics

Rainer Dick

Graduate texts in physics•Jan 1, 2016•7 citations

Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II

Ingrid C. Daubechies, John R. Klauder

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.

Journal of Mathematical Physics•Sep 1, 1985•101 citations
The overcompleteness of the coherent states for the Heisenberg–Weyl group implies that many different integral kernels can be used to represent the same operator. Within such an equivalence class we construct an integral kernel to represent the quantum-mechanical evolution operator for certain dynamical systems in the form of a path integral that involves genuine (Wiener) measures on continuous phase-space paths. To achieve this goal it is necessary to employ an expression for the classical action different from the usual one.
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.