Algebraic and geometric aspects of generalized quantum dynamics

TL;DR

This paper explores the algebraic and geometric structures underlying generalized quantum dynamics, focusing on non-commutative phase space and generalized Poisson brackets, drawing parallels with classical mechanics.

Contribution

It introduces algebraic and geometric frameworks for generalized quantum dynamics, highlighting properties analogous to classical Poisson brackets and symplectic structures.

Findings

Identifies algebraic structures of generalized Poisson brackets

Describes geometric aspects of non-commutative phase space

Draws parallels between quantum and classical phase space properties

Abstract

\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and ordinary symplectic structure.