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

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.