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Background fermion condensates in a landscape dominated by global SUSY are reassessed in connection with a scenario where Lorentz symmetry is violated in the bosonic sector (actually, the photon sector) by a $CPT$-even $k_F$-term. An effective photonic action is discussed that originates from the supersymmetric background fermion condensates. Also, the photino mass emerges in terms of a particular condensate contrary to what happens in the $k_{AF}$-violation. Finally, the interparticle potential induced by the effective photonic action is investigated and a confining profile is identified., Comment: 14 pages. arXiv admin note: text overlap with arXiv:1102.3777 by other authors

We present an N=1 supersymmetric generalization of the Maximal Abelian Gauge (MAG) in its superfield and component-field formulations, and discuss its Faddeev-Popov quantization, the associated BRST symmetry and the corresponding Slavnov-Taylor identity in superspace approach., Comment: 11 pages, no figures

Over the recent decades, diverse formalisms have emerged that are adopted to approach complex systems. Amongst those, we may quote the q-calculus in Tsallis' version of Non-Extensive Statistics with its undeniable success whenever applied to a wide class of different systems; Kaniadakis' approach, based on the compatibility between relativity and thermodynamics; Fractional Calculus (FC), that deals with the dynamics of anomalous transport and other natural phenomena, and also some local versions of FC that claim to be able to study fractal and multifractal spaces and to describe dynamics in these spaces by means of fractional differential equations. The question we might ask is whether or not there are common aspects that connect these alternative approaches. In this short communication, we discuss a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with local form of fractional-derivative operators defined in fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. This connection opens up new perspectives for theories that satisfactorily describe the dynamics for the transport in media with fractal metrics, such as porous or granular media. Possible connections with other alternative definitions of FC are also contempled. Insights on complexity connected to concepts like coarse-grained space-time and physics in general are pointed out., Comment: 12 pages. Original Article

This paper sets out to establish a comparative study between classes of spin- and velocity-dependent potentials for spin-1/2 and spin-1 matter currents/sources in the non-relativistic regime. Both (neutral massive) scalar and vector particles are considered to mediate the interactions between (pseudo-)scalar sources or (pseudo-)vector currents. Though our discussion is more general, we contemplate specific cases in which our results may describe the electromagnetic interaction with a massive (Proca-type) photon exchanged between two spin-1/2 or two spin-1 carriers. We highlight the similarities and peculiarities of the potentials for the two different types of charged matter and also focus our attention on the comparison between the particular aspects of two different field representations for spin-1 matter particles. We believe that our results may contribute to a further discussion of the relation between charge, spin and extensibility of elementary particles., Comment: In this version (v5), a Corrigendum has been added after the published paper

We investigate the role played by particular field representations of an intermediate massive spin-1 boson in the context of spin-dependent interparticle potentials between fermionic sources in the limit of low momentum transfer. The comparison between the well-known case of the Proca field and that of an exchanged spin-1 boson (with gauge-invariant mass) described by a 2-form potential mixed with a 4-vector gauge field is established in order to pursue an analysis of spin- as well as velocity-dependent profiles of the interparticle potentials. We discuss possible applications and derive an upper bound on the product of vector and pseudo-tensor coupling constants., Comment: 23 pages, 2 figures

We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing between a $U(1)$ potential and an Abelian 3-form field by means of a topological mass term. An extended covariant derivative is introduced to minimally couple a Dirac field to the $U(1)$ potential, while this same covariant derivative non-minimally couples the 3-form field to the charged fermion. A number of properties are discussed in 5D; in particular, the appearance of a topological fermionic current. A 4-dimensional reduced version of the model is investigated and, { \bf in addition to the $U(1)$ electric- and magnetic-sort of fields,} there emerges an extra set of electric- and magnetic-like fields which contribute a negative pressure and may be identified as a possible fraction of dark energy. The role of the topological fermionic current is also contemplated upon dimensional reduction from 5D to 4D. Other issues we present in 4 space-time dimensions are the emergence {\bf of a pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf which we interpret as a kind of paraphoton}, and the calculation of spin- and velocity-dependent interparticle potentials associated to the exchange of the intermediate bosonic fields of the model., Comment: -- 30 pages -- L. P. R. Ospedal appears as a new co-author; modifications by inclusion of the gravitational sector and the attainment of a spin- and velocity-dependent potential as an application have been worked out in this Revised Version

In this work, we investigate aspects of the electron, muon and tau gyromagnetic ratios (g-factor) in a fractional coarse-grained scenario, by adopting a Modified Riemann-Liouville (MRL) fractional calculus. We point out the possibility of mapping the experimental values of the specie's g-factors into a theoretical parameter which accounts for fractionality, without computing higher-order QED calculations. We wish to understand whether the value of (g-2) may be traced back to a fractionality of space-time.The justification for the difference between the experimental and the theoretical value g=2 stemming from the Dirac equation is given in the terms of the complexity of the interactions of the charged leptons, considered as pseudo-particles and "dressed" by the interactions and the medium. Stepwise, we build up a fractional Dirac equation from the fractional Weyl equation that, on the other hand, was formulated exclusively in terms of the helicity operator. From the fractional angular momentum algebra, in a coarse-grained scenario, we work out the eigenvalues of the spin operator. Based on the standard electromagnetic current, as an analogy case, we write down a fractional Lagrangian density, with the electromagnetic field minimally coupled to the particular charged lepton. We then study a fractional gauge-like invariance symmetry, formulate the covariant fractional derivative and propose the spinor field transformation. Finally, by taking the non-relativistic regime of the fractional Dirac equation, the fractional Pauli equation is obtained and, from that, an explicit expression for the fractional g-factor comes out that is compared with the experimental CODATA value. Our claim is that the different lepton species must probe space-time by experiencing different fractionalities, once the latter may be associated to the effective interactions of the different families with the medium., Comment: 15 pages

We study the spectrum of the minimal supersymmetric extension of the Carroll-Field-Jackiw model for Electrodynamics with a topological Chern-Simons-like Lorentz-symmetry violating term. We identify a number of independent background fermion condensates, work out the gaugino dispersion relation and propose a photonic effective action to consider aspects of confinement induced by the SUSY background fermion condensates, which also appear to signal Lorentz-symmetry violation in the photino sector of the action. Our calculations of the static potential are carried out within the framework of the gauge-invariant but path-dependent variables formalism which are alternative to the Wilson loop approach. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges., Comment: 11 pages, photino dispersion relation is extended to included the case the photino acquires mass through spontaneous SUSY breaking

In this work, we adopt the simplest model that spontaneously breaks supersymmetry, namely, the minimal O'Raifeartaigh model. The effective potential is computed in the framework of the linear delta expansion (LDE) approach up to the order $\delta^2$, conjugated with superspace and supergraph techniques. The latter can be duly mastered even if supersymmetry is no longer exact and the efficacy of the superfield approach in connection with the LDE procedure is confirmed according to our investigation. That opens up a way for a semi-nonperturbative superspace computation which allows us to deal with spontaneously broken supersymmetric models and encourages us to go further and apply this treatment to the Minimal Supersymmetric Standard Model (MSSM) precision tests., Comment: 42 pages, 22 figures, text modified, new paragraph added in the conclusions, revtex4