Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space

Abstract

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 ${\varphi }^4$ 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.

22 pages. Continuation of 1206.4065 with substantial text overlap. arXiv admin note: substantial text overlap with arXiv:1206.4065

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Cited by in corpus (10)

• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
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• Dirac equation on coordinate dependent noncommutative space-time
• Higgs Couplings in NonCommutative Standard Model
• Faddeev-Jackiw approach of the noncommutative spacetime Podolsky electromagnetic theory
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• The Strong Interaction Model in DFR noncommutative space-time
• Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale
• The standard electroweak model in the noncommutative $DFR$ space-time
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time