Matter Fields in the Lagrangian Loop Representation: Scalar QED

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. We have simulated numerically the loop action equivalent to the Villain form of the action and mapped out the beta-gamma phase diagram of this model.Comment: 10 pages, LaTe

Finite Lattice Hamiltonian Computations in the P-Representation: the Schwinger Model

The Schwinger model is studied in a finite lattice by means of the P-representation. The vacuum energy, mass gap and chiral condensate are evaluated showing good agreement with the expected values in the continuum limit.Comment: 6 pages, 5 eps figures, espcrc

The Lagrangian Loop Representation of Lattice U(1) Gauge Theory

It is showed how the Hamiltonian lattice $loop$ $representation$ can be cast straightforwardly in the Lagrangian formalism. The procedure is general and here we present the simplest case: pure compact QED. This connection has been shaded by the non canonical character of the algebra of the fundamental loop operators. The loops represent tubes of electric flux and can be considered the dual objects to the Nielsen-Olesen strings supported by the Higgs broken phase. The lattice loop classical action corresponding to the Villain form is proportional to the quadratic area of the loop world sheets and thus it is similar to the Nambu string action. This loop action is used in a Monte Carlo simulation and its appealing features are discussed.Comment: 13 pp, UAB-FT-341/9

On the Path Integral Loop Representation of (2+1) Lattice Non-Abelian Theory

A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The corresponding path integral for SU(2) lattice gauge theory is expressed as a sum over colored surfaces, i.e. only involving the $j_p$ attached to the lattice plaquettes. This surfaces may be interpreted as the world sheets of the spin networks In 2+1 dimensions, this can be accomplished by working in a lattice dual to a tetrahedral lattice constructed on a face centered cubic Bravais lattice. On such a lattice, the integral of gauge variables over boundaries or singular lines -- which now always bound three coloured surfaces -- only contributes when four singular lines intersect at one vertex and can be explicitly computed producing a 6-j or Racah symbol. We performed a strong coupling expansion for the free energy. The convergence of the series expansions is quite different from the series expansions which were performed in ordinary cubic lattices. In the case of ordinary cubic lattices the strong coupling expansions up to the considered truncation number of plaquettes have the great majority of their coefficients positive, while in our case we have almost equal number of contributions with both signs. Finally, it is discused the connection in the naive coupling limit between this action and that of the B-F topological field theory and also with the pure gravity action.Comment: 16 pages, REVTEX, 8 Encapsulated Postscript figures using psfig, minor changes in text and reference