Géométrie symplectique et physique mathématique. (French) Zbl 0399.70003
This essay is essentially a survey article in which very many aspects of theoretical physics are very briefly discussed in modern mathematical terminology.
In the first part it is shown how a symplectic manifold is associated with a classical dynamical system; this gives rise to a discussion of Noether’s theorem, mass and symplectic cohomology, thermodynamics and Lie groups.
The second part is concerned with quantization, beginning with physical and geometrical optics leading up to the photoelectric effect. The formal procedure of quantization is described in terms of the formalism developed in the first part.
In the first part it is shown how a symplectic manifold is associated with a classical dynamical system; this gives rise to a discussion of Noether’s theorem, mass and symplectic cohomology, thermodynamics and Lie groups.
The second part is concerned with quantization, beginning with physical and geometrical optics leading up to the photoelectric effect. The formal procedure of quantization is described in terms of the formalism developed in the first part.
Reviewer: Hanno Rund (Toronto)
MSC:
| 70-02 | Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems |
| 53D50 | Geometric quantization |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 70G99 | General models, approaches, and methods in mechanics of particles and systems |
| 37J06 | General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants |
