Path integral action and exact renormalization group dualities for quantum systems in noncommutative plane

TL;DR

This paper uses path integral and renormalization group methods to analyze a noncommutative harmonic oscillator, establishing an equivalence with a commutative system and deriving its ground state spectrum.

Contribution

It introduces a novel approach combining path integrals and exact renormalization group to relate noncommutative and commutative quantum systems.

Findings

Derived the action for the noncommutative harmonic oscillator in coherent state basis.

Established an equivalence between noncommutative and commutative quantum systems.

Obtained the ground state spectrum of the noncommutative oscillator.

Abstract

We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From this the action in the coherent state basis without any additional degrees of freedom is obtained. This gives the ground state spectrum of the system. We then employ the exact renormalization group approach to show that an equivalence can be constructed between this (noncommutative) system and a commutative system.