On external backgrounds and linear potential in three dimensions

For a three-dimensional theory with a coupling $\phi \epsilon ^{\mu \nu \lambda} v_\mu F_{\nu \lambda}$, where $v_\mu$ is an external constant background, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. While in the case of a purely timelike vector the static potential remains Coulombic, in the case of a purely spacelike vector the potential energy is the sum of a Bessel and a linear potentials, leading to the confinement of static charges. This result may be considered as another realization of the known Polyakov's result.Comment: 6 page

Some remarks about gauge-invariant Yang-Mills fields

In order to eliminate gauge variant degrees of freedom we study the way to introduce gauge invariant fields in pure non-Abelian Yang-Mills theory. Our approach is based on the use of the gauge-invariant but path-dependent variables formalism. It is shown that for a special class of paths these fields coincide with the usual ones in some definite gauges. The interquark potential is discussed by exploiting the rich structure of the gluonic cloud or dressing around static fermions.Comment: 14 pages, late

Remarks on the interquark potential in the presence of a minimal length

We calculate the lowest-order corrections to the static potential for both Yang-Mills theory and gluodynamics in curved space-time, in the presence of a quantum gravity induced minimal length. Our analysis is carried out within stationary perturbation theory. As a consequence, the potential energy is the sum of a Yukawa-like potential and a linear potential for gluodynamics in curved space-time, leading to the confinement of static charges. Interestingly enough, we obtain that the coefficient of the linear term ("string tension") is ultraviolet finite. We should highlight the role played by the new quantum of length in our analysis.Comment: 10 pages. Accepted for publication in J. Phys.

Remarks on nonlinear electrodynamics II

We consider both massive Euler-Heisenberg-like and Euler-Heisenberg-like Electrodynamics in the approximation of the strong-field limit. Our analysis shows that massive Euler-Heisenberg-type Electrodynamics displays the vacuum birefringence phenomenon. Afterwards, 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. Interestingly enough, for massive Euler-Heisenbeg-like electrodynamics (Whichmann-Kroll) we obtain a new long-range ($1/r^3$- type) correction, apart from a long-range ($1/r^5$- type) correction to the Coulomb potential. However, Euler-Heisenberg-like Electrodynamics in the approximation of the strong-field limit (to the leading logarithmic order), display a long-range ($1/r^5$- type) correction to the Coulomb potential. Again, for their non-commutative versions, the interaction energy is ultraviolet finite.Comment: 12 pages. Revised version. Title changed. To appear in AHE

Static potential and a new generalized connection in three dimensions

For a recently proposed pure gauge theory in three dimensions, without a Chern-Simons term, we calculate the static interaction potential within the structure of the gauge-invariant variables formalism. The result coincides with that of the Maxwell-Chern-Simons theory in the short distance regime, which shows the confining nature of the potential.Comment: 9 page

Some Considerations About Podolsky-Axionic Electrodynamics

For a Podolsky-axionic electrodynamics, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is equivalent to that of axionic electrodynamics from a new noncommutative approach, up to first order in $\theta$.Comment: 11 page

Remarks on Axion-like models

For a recently proposed alternative to the traditional axion model, we study its long distance behavior, in particular the confinement versus screening issue, and show that a compactified version of this theory can be further mapped into the massive Schwinger model. Our calculation is based on the gauge-invariant but path-dependent variables formalism. This result agrees qualitatively with the usual axion model.Comment: 7 page

Symmetry in noncommutative quantum mechanics

We reconsider the generalization of standard quantum mechanics in which the position operators do not commute. We argue that the standard formalism found in the literature leads to theories that do not share the symmetries present in the corresponding commutative system. We propose a general prescription to specify a Hamiltonian in the noncommutative theory that preserves the existing symmetries. We show that it is always possible to choose this Hamiltonian in such a way that the energy spectrum of the standard and non-commuting theories are identical, so that experimental differences between the predictions of both theories are to be found only at the level of the detailed structure of the energy eigenstates.Comment: 11 pages, Late

Physical and mathematical evidences for a negative-rank tensor

We propose and study the properties of a new potential demanded by the self-consistency of the duality scheme in electromagnetic-like field theories of totally anti-symmetric tensors in diverse dimensions. Physical implications of this new potential is manifest under the presence of scalar condensates in the Julia-Toulouse mechanism for the nucleation of topological defects with consequences for the confinement phenomenon.Comment: 7 page

On condensation of topological defects and confinement

We study the static quantum potential for a theory of anti-symmetric tensor fields that results from the condensation of topological defects, within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static probe charges.Comment: 9 pages, Revtex, no figures. One of us (PG) would like to dedicate this work to the memory of Jian-Jun Yang; a mispelling of a quoted author is correcte