On the quantum dynamics of non-commutative systems

Details On the quantum dynamics of non-commutative systems On the quantum dynamics of non-commutative systems

2007-09-25

arxiv.org/abs/0709.4057v2

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, title changed, version to be published in Brazilian Journal of Physics

Scientific paper

This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and quantum dynamics for the models under investigation. We then elaborate on recently reported results concerned with the sufficient conditions for the existence of the Born series and unitarity and turn, afterwards, into analyzing the functional quantization of non-commutative systems. The compatibility between the operator and the functional approaches is established in full generality. The intricacies arising in connection with the explicit computation of path integrals, for the systems under scrutiny, is illustrated by presenting the detailed calculation of the Feynman kernel for the non-commutative two dimensional harmonic oscillator.

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