Physics NotePublished
The Weyl Representation in Classical and Quantum Mechanics
A. M. Ozorio de Almeida
1996
Publication details
- Authors
- A. M. Ozorio de Almeida
- Type
- Physics Note
- Status
- Published
- Publication date
- 1996
- Description
- The position representation of the evolution operator in quantum mechanics is analogous to the generating function formalism of classical mechanics. Similarly, the Weyl representation is connected to new generating functions described by chords and centres in phase space. Both classical and quantal theories relie on the group of translations and reflections through a point in phase space. The composition of small time evolutions leads to new versions of the classical variational principle and to path integrals in quantum mechanics. The strong resemblance between the two theories allows a clear derivation of the semiclassical limit in which observables evolve classically in the Weyl representation. The restriction of the motion to the energy shell in classical mechanics is the basis for a full review of the semiclassical Wigner function and the theory of scars of periodic orbits. By embedding the theory of scars in a fully uniform approximation, it is shown that the region in which the scar contribution is oscillatory is separated from a decaying region by a caustic that touches the shell along the periodic orbit and widens quadratically within the energy shell.
- Year
- 1996
- Number
- CBPF-NF-062/96
- Linked to a thesis
- No
- Linked to a grant
- No