The authors give an algebraic characterisation of the dynamical systems which preserve the coherence of a generalised coherent state defined for a Lie group. The breaking of coherence is related to singularities appearing in the S matrix. They show a regularisation procedure to eliminate such singularities based on the jet realisation of the diffeomorphism group induced by contact transformations on the state manifold.

https://iopscience.iop.org/article/10.1088/0305-4470/18/9/013/pdf

Stability of coherent states

A classification theory for quantizable dynamical systems

The Morse index is studied in the theory of canonical quantization of dynamical systems. Standard results on the Hodge index and vanishing theorems are translated into the language of quantizable dynamical systems.

Remarks on Morse Theory in Canonical Quantization

Examples in quantizable dynamical systems

In a previous research we have shown that the KS-transformation, developed by Kustaanheimo and Stiefel for the regularization of the Kepler problem, may be interpreted as the correspondence which associates to each null 4-vector of the space of Minkowski a one-index spinor, defined up to a phase factor, and we have obtained a new form of the KS-transformation. In the present research we show that this formulation allows a straight derivation of the Hopf fibering of the sphere S3 (characterized by unit spinors) having the base space given by the section (sphere S2) of the light cone, and we show that the KS-transformation allows the ≪quantization of the symplectic manifold S2≫ in the sense of Souriau. The sphere S3 turns out to be a ≪contact≫ quantized manifold. The ≪bilinear relation≫ characteristic of the KS-theory and the column vectors of the KS-matrix are intimately related to the contact structure.

The Kepler problem spinor regularization and quantization on the manifolds S2

Differential geometric concepts in canonical quantization are discussed. Souriau'sespace fibre quantifiant is shown under certain conditions to be realized in contact structure. Illustrative examples of contact structures are examined.

N. E. Hurt

Papers

Remarks on canonical quantization