Unitary Quantum Physics with Time-Space Noncommutativity

Details Unitary Quantum Physics with Time-Space Noncommutativity Unitary Quantum Physics with Time-Space Noncommutativity

2004-06-14

arxiv.org/abs/hep-th/0406125v3

JHEP0410:072,2004

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, published version

Scientific paper

10.1088/1126-6708/2004/10/072

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 Schrodinger equation is studied. We prove in particular the following: suppose the Hamiltonian of a quantum mechanical particle on spacetime 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 commutative and noncommutative versions of the Hamiltonian have identical spectra.

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