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Unitary quantum physics with time-space noncommutativity

Aiyalam P. Balachandran et al JHEP10(2004)072   doi: 10.1088/1126-6708/2004/10/072  Help

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Aiyalam P. Balachandran1, Thupil R. Govindarajan2, Carlos Molina Mendes3 and Paulo Teotonio-Sobrinho3
1 Physics Department, Syracuse University, Syracuse, NY, 13244-1130, U.S.A.
2 The Institute of Mathematical Sciences, C.I.T. Campus Taramani, Chennai 600 113, India
3 Instituto de Física, Universidade de São Paulo, C.P. 66318, São Paulo, SP, 05315-970, Brazil
E-mail: cmolina@fma.if.usp.br

Abstract. In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrödinger equation is studied. We prove in particular the following: suppose the hamiltonian H of a quantum mechanical particle on spacetime Bbb RN−1 × Bbb R has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the noncommutative version hat H of H and H have identical spectra.

Key words: Field Theories in Lower Dimensions; Non-Commutative Geometry

E-print number: hep-th/0406125
Cited: by
Refers: to

Received 30 July 2004, accepted for publication 28 October 2004
Published 24 November 2004

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