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  Quantum Mechanics on SO(3) via Non-commutative Dual Variables

Oriti, D., & Raasakka, M. (2011). Quantum Mechanics on SO(3) via Non-commutative Dual Variables. Physical Review D, 84(2): 025003. doi:10.1103/PhysRevD.84.025003.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0011-3026-1 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0011-3028-E
Genre: Journal Article

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 Creators:
Oriti, Daniele1, Author              
Raasakka, Matti1, Author              
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,Quantum Physics, quant-ph
 Abstract: We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the non-commutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the non-trivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semi-classical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam models.

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 Dates: 2011-03-102011-03-162011
 Publication Status: Published in print
 Pages: 28 pages; references and one remark added, typos corrected, readability improved
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 Rev. Method: -
 Identifiers: arXiv: 1103.2098
DOI: 10.1103/PhysRevD.84.025003
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 84 (2) Sequence Number: 025003 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258