Geometrical CP violation in multi-Higgs models

We introduce several methods to obtain calculable phases with geometrical values that are independent of arbitrary parameters in the scalar potential. These phases depend on the number of scalars and on the order of the discrete non-Abelian group considered. Using these methods we present new geometrical CP violation candidates with vacuum expectation values that must violate CP (the transformation that would make them CP conserving is not a symmetry of the potential). We also extend to non-renormalisable potentials the proof that more than two scalars are needed to obtain these geometrical CP violation candidates.Comment: 8 pages, 2 figures. v2: table added, accepted by JHE

Causal Structure and Birefringence in Nonlinear Electrodynamics

We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also proof that there is only one analytic nonlinear electrodynamics presenting no birefringence.Comment: 11 pages, no figure

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p>1. Under the assumptions of locality and Poincare invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term.Comment: 17 pages, details of a proof added, accepted for publication in JHE

Functional Bosonization of Non-Relativistic Fermions in (2+1)(2+1) Dimensions

We analyze the universality of the bosonization rules in non-relativistic fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in such a way that the fermionic density maps into a magnetic flux and the fermionic current maps into a transverse electric field. These are universal rules in the sense that they remain valid whatever the interaction considered. We also show that these rules are universal in the case of non-linear dispersion relations provided we consider only density-density interactions. We apply the functional bosonization formalism to a non-relativistic and non-local massive Thirring-like model and evaluate the spectrum of collective excitations in several limits. In the large mass limit, we are able to exactly calculate this spectrum for arbitrary density-density and current-current interactions. We also analyze the massless case and show that it has no collective excitations for any density-density potential in the Gaussian approximation. Moreover, the presence of current interactions may induce a gapless mode with a linear dispersion relation.Comment: 26 Pages, LaTeX, Final version to appear in International Journal of Modern Physics