Path integral action and exact renormalization group dualities for quantum systems in noncommutative plane
Department of Physics, West Bengal State University - Barasat, Kolkata 700126, India Sun Laboratory of Theoretical Physics (SLTP) - A7/5, Karunamoyee Housing Estate, Block ED, and Sector II, Salt Lake, Kolkata 700091, India Inter University Centre for Astronomy and Astrophysics (IUCAA) - Pune 411007, India
Received: 20 February 2015
Accepted: 22 May 2015
We employ the path integral approach developed in Gangopadhyay S. and Scholtz F. E., Phys. Rev. Lett., 102 (2009) 241602 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.
PACS: 11.10.Nx – Noncommutative field theory
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