Perturbed nonlinear models from Noncommutativity

TL;DR

This paper derives a noncommutative version of Newton's Second Law using Ehrenfest's Theorem and explores its implications for discrete systems and field theories.

Contribution

It introduces a novel approach to formulating noncommutative generalizations of field theories based on noncommutative Newtonian dynamics.

Findings

Derived noncommutative Newton's Second Law from Ehrenfest's Theorem.

Constructed noncommutative generalizations of 2D field theories.

Provided insights into the dynamics of systems with noncommutative geometry.

Abstract

By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical evolutions are governed by the noncommutative Newton's Second Law we have constructed some alternative noncommutative generalizations of two-dimensional field theories.