New parameters of Non-commutativity in Quantum Mechanics

TL;DR

This paper introduces new parameters to describe non-commutative spaces in quantum mechanics, exploring their properties, relationships with existing methods, and implications for Hamiltonians of free particles.

Contribution

It proposes novel parameters for non-commutativity, linking commutative and non-commutative spaces, and analyzes their effects on quantum systems beyond existing methods.

Findings

New parameters effectively describe non-commutative spaces.

Seiberg-Witten method is insufficient under certain conditions.

Hamiltonian analysis reveals implications of the new parameters.

Abstract

At this paper, it is considered to find a way for defining non-commutative spaces by ordinary commutative ones and vice versa. A novel parameter which has not been considered so far is represented. This parameter describes equivalent spaces. Also, we searched concepts of these new parameters with one problem. Noncommutativity in total space is important here because it could explain more concepts. As we knew SW method (Seiberg-Witten) explained noncommutativity so here, we showed that it was not suitable for some conditions.in the end we considered Hamiltonian of free particle in new noncommutativity and we found concepts of new parameters.