On the Zitterbewegung Transient Regime in a Coarse-Grained Space-Time

In the present contribution, by studying a fractional version of Dirac's equation for the electron, we show that the phenomenon of Zitterbewegung in a coarse-grained medium exhibits a transient oscillatory behavior, rather than a purely oscillatory regime, as it occurs in the integer case, $\alpha=1$. Our result suggests that, in such systems, the Zitterbewegung-type term related to a trembling motion of a quasiparticle is tamed by its complex interactions with other particles and the medium. This can justify the difficulties in the observation of this interesting phenomenon. The possibility that the Zitterbewegung be accompanied by a damping factor supports the viewpoint of particle substructures in Quantum Mechanics.Comment: 11 pages, 1 figure. This paper has been published in J. Adv. Phys. 7 (2015) 144

A note on nonlinear electrodynamics

We explore the physical consequences of a new nonlinear electrodynamics, for which the electric field of a point-like charge is finite at the origin, as in the well-known Born-Infeld electrodynamics. However, contrary to the latter, in this new electrodynamics the phenomenon of birefringence and dichroism take place in the presence of external magnetic fields. Subsequently we study the interaction energy, within the framework of the gauge-invariant but path-dependent variables formalism. Interestingly enough, the static potential profile contains a linear potential leading to the confinement of static charges.Comment: 5 pages. arXiv admin note: substantial text overlap with arXiv:1607.0299

Remarks on nonlinear Electrodynamics

We consider both generalized Born-Infeld and Exponential Electrodynamics. The field-energy of a point-like charge is finite only for Born-Infeld-like Electrodynamics. However, both Born-Infeld-type and Exponential Electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of Electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in long-range ($1/r^5$- type) corrections to the Coulomb potential. Once again, for their non-commutative versions, the interaction energy is ultraviolet finite.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.515

(1+3)(1+3)D topological superconductors: screening and confinement in presence of external fields

Adopting the gauge-invariant and path-dependent variables formalism, we compute the interaction energy for a topological field theory describing $(1+3)$D topological superconductors in presence of external fields. As a result, in the case of a constant electric field- strength expectation value, we show that the interaction energy describes a purely screening phase, encoded in a Yukawa potential. On the other hand, in the case of a constant magnetic field-strength and for a very small Josephson coupling constant, the particle-antiparticle binding potential displays a linear term leading to the confinement of static charge probes along with a screening contribution.Comment: 6 page

Remarks on the static potential in theories with Lorentz violation terms

We study the impact of Lorentz violating terms on a physical observable for both electrodynamics of chiral matter and an Abelian Higgs-like model in $3+1$ dimensions. Our calculation is done within the framework of the gauge-invariant, but path-dependent, variables formalism. Interestingly enough, for electrodynamics of chiral matter we obtain a logarithmic correction to the usual static Coulomb potential. Whereas for a Abelian Higgs model with a Lorentz-breaking term, our result displays new corrections to the Yukawa potential.Comment: 7 page

Remarks on a B∧FB \wedge F model with topological mass from gauging spin

Aspects of screening and confinement are reassessed for a $B \wedge F$ model with topological mass with the gauging of spin. Our discussion is carried out using the gauge-invariant, but path-dependent, variables formalism. We explicitly show that the static potential profile is the sum of a Yukawa and a linear potential, leading to the confinement of static external charges. Interestingly enough, similar results are obtained in a theory of antisymmetric tensor fields that results from the condensation of topological defects as a consequence of the Julia-Toulouse mechanism.Comment: 5 page

Topological Gravity on (D,N)−(D,N)-Shift Superspace Formulation

In this contribution, we re-assess the subject of topological gravity by following the Shift Supersymmetry formalism. The gauge-fixing of the theory goes under the Batallin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and anti-ghost superfields, associated to the super-vielbein and the super-Lorentz connection. We extend the formulation of the topological gravity action to an arbitrary number of dimensions of the shift superspace by adopting a formulation based on the gauge-fixing for BF-type models