34 research outputs found
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
Canonical formulation of N = 2 supergravity in terms of the Ashtekar variable
We reconstruct the Ashtekar's canonical formulation of N = 2 supergravity
(SUGRA) starting from the N = 2 chiral Lagrangian derived by closely following
the method employed in the usual SUGRA. In order to get the full graded algebra
of the Gauss, U(1) gauge and right-handed supersymmetry (SUSY) constraints, we
extend the internal, global O(2) invariance to local one by introducing a
cosmological constant to the chiral Lagrangian. The resultant Lagrangian does
not contain any auxiliary fields in contrast with the 2-form SUGRA and the SUSY
transformation parameters are not constrained at all. We derive the canonical
formulation of the N = 2 theory in such a manner as the relation with the usual
SUGRA be explicit at least in classical level, and show that the algebra of the
Gauss, U(1) gauge and right-handed SUSY constraints form the graded algebra,
G^2SU(2)(Osp(2,2)). Furthermore, we introduce the graded variables associated
with the G^2SU(2)(Osp(2,2)) algebra and we rewrite the canonical constraints in
a simple form in terms of these variables. We quantize the theory in the
graded-connection representation and discuss the solutions of quantum
constraints.Comment: 19 pages, Latex, corrected some typos and added a referenc
The Lagrangian Loop Representation of Lattice U(1) Gauge Theory
It is showed how the Hamiltonian lattice 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
Introduction to supersymmetric spin networks
In this paper we give a general introduction to supersymmetric spin networks.
Its construction has a direct interpretation in context of the representation
theory of the superalgebra. In particular we analyze a special kind of spin
networks with superalgebra . It turns out that the set of
corresponding spin network states forms an orthogonal basis of the Hilbert
space \cal L\mit^2(\cal A\mit/\cal G), and this argument holds even in the
q-deformed case. The spin networks are also discussed briefly. We
expect they could provide useful techniques to quantum supergravity and gauge
field theories from the point of non-perturbative view.Comment: 27 pages, 16 eps figures. Based on the talk given at Marcel Grossmann
Meeting IX in Rom
Quantum geometry with intrinsic local causality
The space of states and operators for a large class of background independent
theories of quantum spacetime dynamics is defined. The SU(2) spin networks of
quantum general relativity are replaced by labelled compact two-dimensional
surfaces. The space of states of the theory is the direct sum of the spaces of
invariant tensors of a quantum group G_q over all compact (finite genus)
oriented 2-surfaces. The dynamics is background independent and locally causal.
The dynamics constructs histories with discrete features of spacetime geometry
such as causal structure and multifingered time. For SU(2) the theory satisfies
the Bekenstein bound and the holographic hypothesis is recast in this
formalism.Comment: Latex 33 pages, 7 Figure, epsfi
A candidate for a background independent formulation of M theory
A class of background independent membrane field theories are studied, and
several properties are discovered which suggest that they may play a role in a
background independent form of M theory. The bulk kinematics of these theories
are described in terms of the conformal blocks of an algebra G on all oriented,
finite genus, two-surfaces. The bulk dynamics is described in terms of causal
histories in which time evolution is specified by giving amplitudes to certain
local changes of the states. Holographic observables are defined which live in
finite dimensional states spaces associated with boundaries in spacetime. We
show here that the natural observables in these boundary state spaces are, when
G is chosen to be Spin(D) or a supersymmetric extension of it, generalizations
of matrix model coordinates in D dimensions. In certain cases the bulk dynamics
can be chosen so the matrix model dynamics is recoverd for the boundary
observables. The bosonic and supersymmetric cases in D=3 and D=9 are studied,
and it is shown that the latter is, in a certain limit, related to the matrix
model formulation of M theory. This correspondence gives rise to a conjecture
concerning a background independent form of M theory in terms of which
excitations of the background independent membrane field theory that correspond
to strings and D0 branes are identified.Comment: Latex 46 pages, 21 figures, new results included which lead to a
modification of the statement of the basic conjecture. Presentation improve
Caracterización de la nutrición mineral en establecimientos ganaderos. [Resumen].
Este trabajo realizado en verano del 2016-17, tuvo como objetivo caracterizar posibles problemas de nutrición mineral en 15 establecimientos.Los establecimientos integraban el proyecto Mejora de la ganadería familiar uruguaya y estaban ubicados en las principales zonas agroecológicas dedicadas a la ganadería. Eran sistemas criadores casi exclusivamente sobre campo natural, con superficies de pastoreo desde 140 a 900 ha