Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime

Abstract

The framework Doplicher-Fredenhagen-Roberts (DFR) of a noncommutative (NC) space-time is considered as a alternative approach to study the NC space-time of the early Universe. In this formalism, the parameter of noncommutative ${\theta }^{\mu \nu }$ is promoted to a coordinate of the space-time, and consequently, we are describing a field theory in a space-time with extra-dimension. Consequently, there is a canonical momentum associated to this new coordinate in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimension. The Fourier space of this framework is automatically extended by the addition of new momenta components. The main concept that we would like 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. When the components of the new momentum are zero, the DFR approach is reduced to the usual NC case, in which ${\theta }^{\mu \nu }$ is a antisymmetric constant matrix. We study a scalar field action with self-quartic interaction ${\varphi }^4\star$ defined in the DFR NC spacetime, obtaining the Feynman rules in the Fourier space for the scalar propagator and vertex of the model. With these rules we are able to build out the radiative corrections to one loop order for the model propagator. The influence of the NC scale, as well as the propagation of the field in the extra-dimension, are analyzed in the ultraviolet divergences scenario. We investigate the actual possibility if this ${\theta }^{\mu \nu }$ conjugate momentum has the property of healing the mixing IR/UV divergences that emerges in this recently new NC spacetime quantum field theory.

20 pages. Pre-print format. arXiv admin note: substantial text overlap with arXiv:1212.4118, arXiv:1206.4065

References in corpus (12)

• Symmetry, Gravity and Noncommutativity
• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Noncommutative Gravity
• Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories
• Dynamical symmetries in noncommutative theories
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Fermions and noncommutative theories
• Tensor Coordinates in Noncommutative Mechanics
• Analytical and numerical analysis of a rotational invariant D=2 harmonic oscillator in the light of different noncommutative phase-space configurations
• Noncommutative Quantum Mechanics with Path Integral
• Path Integral Approach to Noncommutative Quantum Mechanics

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• 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
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• The standard electroweak model in the noncommutative $DFR$ space-time
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