Unitary Quantum Physics with Time-Space Noncommutativity

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 R N −1 × 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 versionĤ of H and H have identical spectra.

Twisted statistics inκ-Minkowski spacetime

“…Hence, unlike in the Moyal case [29], parity is a symmetry of the κ-deformed Minkowski space. The time reversal operator T , which is anti-linear, is defined by…”

“…For the Moyal plane with space-time noncommutativity these issues have been discussed in [29]. Let us consider a system described by the κ-deformed Minkowski space (31).…”

Waves on noncommutative spacetimes

“…The formulation of unitary qf t ′ s when θ 0i = 0 is nontrivial and was carefully done already by Doplicher et al [1]. In recent papers [4,5], Balachandran et al formulated unitary quantum mechanics when θ 0i = 0 basing themselves on the ideas of Doplicher et al Consequences of spacetime noncommutativity in the quantum mechanics of atoms and molecules have been explored by Balachandran and Pinzul [6].…”

“…As explained in detail in Balachandran et al [4], in the former approach, the amount τ of time translation is not "coordinate time", the eigenvalue ofx 0 . For θ = 0, these two could be identified, while for θ = 0,x 0 is an operator not commuting withx 1 , and cannot be interchanged with τ .…”

Using an intense laser beam in interaction with muon/electron beam to probe the noncommutative QED

“…Although the time-space component of the NC parameter has some problems with the unitarity, the quantum mechanics can become unitary in some cases for the time-like part of NC-parameter too [51,52]. In the both approaches besides the corrections on the usual vertices new couplings also appear in comparison with the ordinary standard model.…”