Conformal symplectic geometry, deformations, rigidity and geometrical (KMS) conditions. (English) Zbl 0589.53037

Basart, Henri; Lichnerowicz, André

Lett. Math. Phys. 10, 167-177 (1985).

From the authors’ introduction: ”In Part I, we define and study the notion of the \(*^ f\)-product in a general context and show how the conformal Poisson geometry or symplectic geometry necessarily appears. In Part II, we study the deformations of a \(*^ f\)-product on a symplectic manifold and prove a rigidity theorem in the framework of \(*^ f\)- products (f fixed). We can, however, deform a star product in suitable \(*^ f\)-products, but then we have no equivalence property. We translate this result in terms of statistical mechanics and thus obtain a correct generalization of our results in C. R. Acad. Sci., Paris, Sér. I 293, 347-350 (1981; Zbl 0482.58037).”

Reviewer: A.Verona

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
58H15	Deformations of general structures on manifolds
53D50	Geometric quantization

Keywords:

local associative algebra; conformal Poisson geometry; symplectic geometry; rigidity theorem; star product

Citations:

Zbl 0482.58037

References:

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