Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-09-17
JHEP 0701:073,2007
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, JHEP3 style; minor changes; Published in JHEP
Scientific paper
10.1088/1126-6708/2007/01/073
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry.
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