Consistent Deformed Bosonic Algebra in Noncommutative Quantum Mechanics

TL;DR

This paper investigates a consistent deformed bosonic algebra in two-dimensional noncommutative space, establishing a relation between parameters and constructing a Fock space where noncommutativity effects are parameterized.

Contribution

It introduces a consistent deformed bosonic algebra in noncommutative quantum mechanics and constructs a Fock space with effects represented by parameters.

Findings

Derived a relation between noncommutative parameters for algebra consistency

Constructed a Fock space where noncommutative effects are parameterized

Showed calculations are similar to commutative space

Abstract

In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, the consistent deformed bosonic algebra at the non-perturbation level described by the deformed annihilation and creation operators is investigated. A general relation between noncommutative parameters is fixed from the consistency of the deformed Heisenberg - Weyl algebra with the deformed bosonic algebra. A Fock space is found, in which all calculations can be similarly developed as if in commutative space and all effects of spatial noncommutativity are simply represented by parameters.