2012/12/17 by Everton M. C. Abreu, Mario J. Neves · 1 citation
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1142/s0217751x13500176
22 pages. Continuation of 1206.4065 with substantial text overlap. arXiv admin note: substantial text overlap with arXiv:1206.4065
arxiv created 2012/12/17 · arxiv updated 2015/06/12
We obtained the Feynman propagators for a noncommutative (NC) quantum mechanics defined in the recently developed Doplicher-Fredenhagen-Roberts-Amorim (DFRA) NC background that can be considered as an alternative framework for the NC spacetime of the early Universe. The operators formalism was revisited and we applied its properties to obtain a NC transition amplitude representation. Two examples of DFRA's systems were discussed, namely, the NC free particle and NC harmonic oscillator. The spectral representation of the propagator gave us the NC wave function and energy spectrum. We calculated the partition function of the NC harmonic oscillator and the distribution function. Besides, the extension to NC DFRA quantum field theory is straightforward and we used it in a massive scalar field. We had written the scalar action with self-interaction ϕ4 using the Weyl-Moyal product to obtain the propagator and vertex of this model needed to perturbation theory. %and the effective action to give rise one-particle-irreducible diagrams. It is important to emphasize from the outset is that the formalism demonstrated here will not be constructed introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. In this extra dimensional NC space, we presented also the idea of dimensional reduction to recover commutativity.