From Noncommutative Phase Space to Hilbert Space
- Saha Institute of Nuclear Physics, 1/AF, Bidhan nagar, Kolkata-700 064 (India)
In the Hamiltonian formulation, classical mechanics employs the commutative algebra of functions that are defined on phase space a point of which could be represented using Dirac delta distributions. In the absence of such a concrete existence of the notion of point in the quantum domain, we show how the quantum mechanical formalism emerges by replacing the commutative algebra by a noncommutative algebra of functions and introducing the quantum condition. The noncommutativity is achieved by deforming the product of two functions and by introducing the Moyal brackets, the basic Moyal brackets between two spatial coordinates and between position and momentum coordinates being noncommutative. The only other input we make use of is the quantum condition which is motivated from its classical analogue--the square of Dirac delta distributions.
- OSTI ID:
- 21035978
- Journal Information:
- AIP Conference Proceedings, Vol. 939, Issue 1; Conference: International workshop on theoretical high energy physics, Roorkee (India), 15-20 Mar 2007; Other Information: DOI: 10.1063/1.2803828; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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