Noncommutative Harmonic Oscillator at Finite Temperature: A Path Integral Approach

TL;DR

This paper employs a path integral method to analyze a two-dimensional noncommutative harmonic oscillator at finite temperature, confirming the consistency between Lagrangian and Hamiltonian formulations for the partition function.

Contribution

It introduces a path integral approach to compute the partition function of a noncommutative harmonic oscillator, demonstrating equivalence of Lagrangian and Hamiltonian methods.

Findings

Partition function derived using path integral method

Lagrangian and Hamiltonian results are consistent

Provides a framework for finite temperature analysis of noncommutative systems

Abstract

We use the path integral approach to a two-dimensional noncommutative harmonic oscillator to derive the partition function of the system at finite temperature. It is shown that the result based on the Lagrangian formulation of the problem, coincides with the Hamiltonian derivation of the partition function.