2016/05/11 by Sunandan Gangopadhyay, Aslam Halder
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Operator Algebra Research #Formalism (music) #Harmonic oscillator #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Path integral formulation #Quantum Mechanics and Non-Hermitian Physics #Quantum differential calculus #Spectral triple #hep-th #quant-ph
paper · pdf · doi:10.1209/0295-5075/117/10010
published as Euro. Phys. Lett. 117 (2017) 10010 · 9 pages Latex
arxiv created 2016/05/11 · openalex created_date 2016/06/24 · openalex publication_date 2017/01/01 · arxiv updated 2017/03/02 · openalex updated_date 2026/08/05
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum system in the space of Hilbert-Schmidt operators acting on noncommutative configuration space, the path integral action of a particle is derived. It is observed that the action has a similar form to that of a particle in a magnetic field in the noncommutative plane. From this action the energy spectrum is obtained for the free particle and the harmonic-oscillator potential. We also show that the nonlocal nature (in time) of the action yields a second-class constrained system from which the noncommutative Heisenberg algebra can be recovered.