Aiyalam P. Balachandran et al JHEP10(2004)072 doi:10.1088/1126-6708/2004/10/072
Unitary quantum physics with time-space noncommutativity
Aiyalam P. Balachandran1, Thupil R. Govindarajan2, Carlos Molina Mendes3 and Paulo Teotonio-Sobrinho3
Show affiliationsIn 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 
N−1 × 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 
of H and H have identical spectra.
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E-print Number: hep-th/0406125
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Issue 10 (October 2004)
Received 30 July 2004, accepted for publication 28 October 2004
Published 24 November 2004
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Unitary quantum physics with time-space noncommutativity
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