Symplectic Path Intersections and the Leray Index

Gosson, Maurice de; Gosson, Serge de

doi:10.1007/978-1-4612-0011-6_7

Cited by 1 publication

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. For (i) and formula (35) in (iii), see Leray [58], de Gosson [23,28]; formulas (32)-( 34) are obtained by matrix multiplication using (37).…”

Section: Quadratic Fourier Transforms and Generating Functionsmentioning

confidence: 99%

“…However, (44) only defines a projective representation of Sp(n), and not its double covering group; if one wants a true covering group one has to carefully determine the cocycle associated with this projective representation (see Reiter [65] for a detailed analysis). In [23] we have given an analytical construction of this cocycle, and in [30,37,38] we use a topological and cohomological method, using techniques from symplectic geometry (the Leray index, and the notion of signature of a triple of Lagrangian planes, further developed in [28,33]).…”

Section: Quadratic Fourier Transforms and Generating Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Paths of canonical transformations and their quantization

Gosson

2015

Rev. Math. Phys.

View full text Add to dashboard Cite

In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and emphasize the analogies between Hamiltonian flows and quantum propagators; this allows us to verify G. Mackey's observation that quantum mechanics (in its Weyl formulation) is a refinement of Hamiltonian mechanics. We discuss in detail the metaplectic representation, which very explicitly shows the close relationship between classical mechanics and quantum mechanics; the latter emerging from the first by lifting Hamiltonian flows to the double covering of the symplectic group. We also give explicit formulas for the factorization of Hamiltonian flows into simpler flows, and prove a quantum counterpart of these results.

show abstract

“…Proof. For (i) and formula (35) in (iii), see Leray [58], de Gosson [23,28]; formulas (32)-( 34) are obtained by matrix multiplication using (37).…”

Section: Quadratic Fourier Transforms and Generating Functionsmentioning

confidence: 99%