800 research outputs found
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
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
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
Continuum spin foam model for 3d gravity
An example illustrating a continuum spin foam framework is presented. This
covariant framework induces the kinematics of canonical loop quantization, and
its dynamics is generated by a {\em renormalized} sum over colored polyhedra.
Physically the example corresponds to 3d gravity with cosmological constant.
Starting from a kinematical structure that accommodates local degrees of
freedom and does not involve the choice of any background structure (e. g.
triangulation), the dynamics reduces the field theory to have only global
degrees of freedom. The result is {\em projectively} equivalent to the
Turaev-Viro model.Comment: 12 pages, 3 figure
Classical Loop Actions of Gauge Theories
Since the first attempts to quantize Gauge Theories and Gravity in the loop
representation, the problem of the determination of the corresponding classical
actions has been raised. Here we propose a general procedure to determine these
actions and we explicitly apply it in the case of electromagnetism. Going to
the lattice we show that the electromagnetic action in terms of loops is
equivalent to the Wilson action, allowing to do Montecarlo calculations in a
gauge invariant way. In the continuum these actions need to be regularized and
they are the natural candidates to describe the theory in a ``confining
phase''.Comment: LaTeX 14 page
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