Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …

We present a mathematical study of the differentiable deformations of the algebras
associated with phase space. Deformations of the Lie algebra of C∞ functions, defined by …

Wigner's quasi-probability distribution function in phase-space is a special (Weyl)
representation of the density matrix. It has been useful in describing quantum transport in …

A new method for computing path integrals explicitly is developed and applied to problems
in non-relativistic quantum mechanics, such as: wave functions, propagators on …

In this work, we develop a general framework in which Noncommutative Quantum
Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ= ϵ k ij …

Invertible maps from operators of quantum observables onto functions of c-number
arguments and their associative products are first assessed. Different types of maps such as …

We study the uniqueness of higher-spin algebras which are at the core of higher-spin
theories in AdS and of CFTs with exact higher-spin symmetry, ie conserved tensors of rank …

We start with a short exposition of developments in physics and mathematics that preceded,
formed the basis for, or accompanied, the birth of deformation quantization in the seventies …

Ausgehend vom einfachsten Phasenraum (Ê2n, ω0) mit seiner kanonischen Poisson-
Klammer für die Funktionenalgebra C∞(Ê2n) haben wir sowohl eine geometrische als auch …

Calogero-Moser systems, which were originally discovered by specialists in integrable
systems, are currently at the crossroads of many areas of mathematics and within the scope …