Mario J. Neves

GREEN FUNCTIONS IN LORENTZ INVARIANT NONCOMMUTATIVE SPACE–TIME

In this paper we investigated the causality problem present in the recent published work about the Doplicher–Fredenhagen–Roberts–Amorim (DFRA) noncommutative framework which analyzed the complex scalar field. We described the noncommutative Klein–Gordon equation with a source term. Its solution was accomplished through the retarded, advanced and causal Green functions constructed in this noncommutative ten-dimensional DFRA space–time. We believe that this solution constitutes the first step in the elaboration of a quantum field theory using the DFRA formalism where the well known noncommutative parameter from now on is an ordinary coordinate of the system and therefore has a canonical conjugate momentum. We discussed the dimensional reduction of this noncommutative space–time (D = 10) in order to recover commutativity in D = 4 space–time, which is not the usual one in noncommutativity literature.

Self-quartic interaction for a scalar field in an extended DFR noncommutative space–time

Abstract The framework of Doplicher–Fredenhagen–Roberts (DFR) for a noncommutative (NC) space–time is considered as an alternative approach to study the NC space–time of the early Universe. Concerning this formalism, the NC constant parameter, θ μ ν , is promoted to coordinate of the space–time and consequently we can describe a field theory in a space–time with extra-dimensions. We will see that there is a canonical momentum associated with this new coordinate in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimensions. The Fourier space of this framework is automatically extended by the addition of the 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 by introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. We will review that when the components of the new momentum are zero, the (extended) DFR approach is reduced to the usual (canonical) NC case, in which θ μ ν is an antisymmetric constant matrix. In this work we will study a scalar field action with self-quartic interaction ϕ 4 ⋆ defined in the DFR NC space–time. We will obtain the Feynman rules in the Fourier space for the scalar propagator and vertex of the model. With these rules we are able to build the radiative corrections to one loop order of the model propagator. The consequences of the NC scale, as well as the propagation of the field in extra-dimensions, will be analyzed in the ultraviolet divergences scenario. We will investigate about the actual possibility that this k μ ν conjugate momentum has the property of healing the combination of IR/UV divergences that emerges in this recently new NC spacetime quantum field theory.

Spontaneous symmetry breaking and masses numerical results in Doplicher-Fredenhagen-Roberts noncommutative space-time

With the elements of the Doplicher-Fredenhagen-Roberts (DFR) noncommutative formalism, we have constructed a standard electroweak model. We have introduced the spontaneous symmetry breaking and the hypercharge in DFR framework. The electroweak symmetry breaking was analyzed and the masses of the new bosons were computed.

Complex-mass shell renormalization of the higher-derivative electrodynamics

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron–positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed.

Strong interaction model in DFR noncommutative space–time

The Doplicher–Fredenhagen–Roberts (DFR) framework for noncommutative (NC) space–times is considered as an alternative approach to describe the physics of quantum gravity, for instance. In this formalism, the NC parameter, i.e. 𝜃μν, is promoted to a coordinate of a new extended space–time. Consequently, we have field theory in a space–time with spatial extra-dimensions. This new coordinate has a canonical momentum associated, where the effects of a new physics can emerge in the fields propagation along the extra-dimension. In this paper, we introduce the gauge invariance in the DFR NC space–time by the composite symmetry U⋆(N) × U⋆(N). We present the non-Abelian gauge symmetry in DFR formalism and the consequences of this symmetry in the presence of such extra-dimension. The gauge symmetry in this DFR scenario can reveal new gauge fields attached to 𝜃-extra-dimension. As application, we construct a unification of Strong Interaction with the electromagnetism and a Higgs model to give masses to the NC bosons. We estimate their masses by using some experimental constraints of QCD.

The standard electroweak model in the noncommutative DFR space–time

The noncommutative (NC) framework elaborated by Doplicher, Fredenhagen and Roberts (DFR) has a Lorentz invariant spacetime structure in order to be considered as a candidate to understand the physics of the early Universe. In DFR formalism the NC parameter (

SOME ASPECTS OF QUANTUM MECHANICS AND FIELD THEORY IN A LORENTZ INVARIANT NONCOMMUTATIVE SPACE

\theta^{\mu\nu}

TeV- and MeV-physics out of an

) is a coordinate operator in an extended Hilbert space and it has a conjugate momentum. Since

SU_{L}(2)\times U_{R}(1)_{J} \times U(1)_{K}

x

model

and