Time dependent transformations in deformation quantization

Time dependent transformations in deformation quantization

We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations. This result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it po...

Deformation Quantization

1. INTRODUCTION Quantum mechanics is often distinguished from classical mechanics by a statement to the effect that the observables in quantum mechanics, unlike those in classical mechanics, do not commute with one another. Yet classical mechanics is meant to give a description (with less precision) of the same physical world as is described by quantum mechanics. One mathematical transcription ...

Graph complexes in deformation quantization

Kontsevich’s formality theorem and the consequent star-product formula rely on the construction of an L∞-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential grade...

Nonperturbative effects in deformation quantization

The Cattaneo-Felder path integral form of the perturbative Kontsevich deformation quantization formula is used to explicitly demonstrate the existence of nonperturbative corrections to näıve deformation quantization. The physical context of the formal problem of deformation quantization is the original one set out by Dirac [1] in making the substitution

Creep: Time‐dependent brittle deformation in rocks