Asymptotic States in Non-Local Field Theories

Asymptotic states in field theories containing non-local kinetic terms are analyzed using the canonical method, naturally defined in Minkowski space. We apply our results to study the asymptotic states of a non-local Maxwell-Chern-Simons theory coming from bosonization in 2+1 dimensions. We show that in this case the only asymptotic state of the theory, in the trivial (non-topological) sector, is the vacuum.Comment: 10 pages, LaTe

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

Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group

In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down through infrared divergent contributions originating from naively irrelevant operators. In particular, we show that the correct fixed point has the form of an array of sliding Luttinger liquids which is free from superficially "irrelevant operators". Similar considerations apply to all theories with sliding symmetries.Comment: 7 pages, 3 figure

Vacuum state of the quantum string without anomalies in any number of dimensions

We show that the anomalies of the Virasoro algebra are due to the asymmetric behavior of raising and lowering operators with respect to the ground state of the string. With the adoption of a symmetric vacuum we obtain a non-anomalous theory in any number of dimensions. In particular for D=4.Comment: 14 pages, LaTex, no figure

The static potential in QED3_3 with non-minimal coupling

Here we study the effect of the non-minimal coupling j^{\mu}\eps \partial^{\nu} A^{\alpha} on the static potential in multiflavor QED$_3$. Both cases of four and two components fermions are studied separately at leading order in the $1/N$ expansion. Although a non-local Chern-Simons term appears, in the four components case the photon is still massless leading to a confining logarithmic potential similar to the classical one. In the two components case, as expected, the parity breaking fermion mass term generates a traditional Chern-Simons term which makes the photon massive and we have a screening potential which vanishes at large inter-charge distance. The extra non-minimal couplings have no important influence on the static potential at large inter-charge distances. However, interesting effects show up at finite distances. In particular, for strong enough non-minimal coupling we may have a new massive pole in the photon propagator while in the opposite limit there may be no poles at all in the irreducible case. We also found that, in general, the non-minimal couplings lead to a finite range {\bf repulsive} force between charges of opposite signs.Comment: 19 pages and 7 figure