48 research outputs found
Vertex Operators for the BF System and its Spin-Statistics Theorems
Let and be two forms,
being the field strength of an abelian connection . The
topological system is given by the integral of . With "kinetic
energy'' terms added for and , it generates a mass for thereby
suggesting an alternative to the Higgs mechanism, and also gives the London
equations. The action, being the large length and time scale limit of this
augmented action, is thus of physical interest. In earlier work, it has been
studied on spatial manifold with boundaries , and
the existence of edge states localised at has been
established. They are analogous to the conformal family of edge states to be
found in a Chern-Simons theory in a disc. Here we introduce charges and
vortices (thin flux tubes) as sources in the system and show that they
acquire an infinite number of spin excitations due to renormalization, just as
a charge coupled to a Chern-Simons potential acquires a conformal family of
spin excitations. For a vortex, these spins are transverse and attached to each
of its points, so that it resembles a ribbon. Vertex operators for the creatin
of these sources are constructed and interpreted in terms of a Wilson integral
involving and a similar integral involving . The standard
spin-statistics theorem is proved for this sources. A new spin-statistics
theorem, showing the equality of the ``interchange'' of two identical vortex
loops and rotation of the transverse spins of a constituent vortex, is
established. Aharonov-Bohm interactions of charges and vortices are studied.
The existence of topologically nontrivial vortex spins is pointed out and their
vertexComment: Latex, 64 pages, SU-4240-516 (plus 1 uuencoded compressed tar file
with the figures) Figures correcte
Discretized Laplacians on an Interval and their Renormalization Group
The Laplace operator admits infinite self-adjoint extensions when considered
on a segment of the real line. They have different domains of essential
self-adjointness characterized by a suitable set of boundary conditions on the
wave functions. In this paper we show how to recover these extensions by
studying the continuum limit of certain discretized versions of the Laplace
operator on a lattice. Associated to this limiting procedure, there is a
renormalization flow in the finite dimensional parameter space describing the
dicretized operators. This flow is shown to have infinite fixed points,
corresponding to the self-adjoint extensions characterized by scale invariant
boundary conditions. The other extensions are recovered by looking at the other
trajectories of the flow.Comment: 23 pages, 2 figures, DSF-T-28/93,INFN-NA-IV-28/93, SU-4240-54
Edge States in 4D and their 3D Groups and Fields
It is known that the Lagrangian for the edge states of a Chern-Simons theory
describes a coadjoint orbit of a Kac-Moody (KM) group with its associated
Kirillov symplectic form and group representation. It can also be obtained from
a chiral sector of a nonchiral field theory. We study the edge states of the
abelian system in four dimensions (4d) and show the following results in
almost exact analogy: 1) The Lagrangian for these states is associated with a
certain 2d generalization of the KM group. It describes a coadjoint orbit of
this group as a Kirillov symplectic manifold and also the corresponding group
representation. 2) It can be obtained from with a ``self-dual" or
``anti-self-dual" sector of a Lagrangian describing a massless scalar and a
Maxwell field [ the phrase ``self-dual" here being used essentially in its
sense in monopole theory]. There are similar results for the nonabelian
system as well. These shared features of edge states in 3d and 4d suggest that
the edge Lagrangians for systems are certain natural generalizations of
field theory Lagrangians related to KM groups.Comment: 12 pages, SU-4240-42
Quasi-Topological Quantum Field Theories and Lattice Gauge Theories
We consider a two parameter family of gauge theories on a lattice
discretization of a 3-manifold and its relation to topological field
theories. Familiar models such as the spin-gauge model are curves on a
parameter space . We show that there is a region of
where the partition function and the expectation value of the
Wilson loop for a curve $\gamma$ can be exactly computed. Depending on the
point of $\Gamma_0$, the model behaves as topological or quasi-topological. The
partition function is, up to a scaling factor, a topological number of $M$. The
Wilson loop on the other hand, does not depend on the topology of $\gamma$.
However, for a subset of $\Gamma_0$, depends on the size of
and follows a discrete version of an area law. At the zero temperature
limit, the spin-gauge model approaches the topological and the
quasi-topological regions depending on the sign of the coupling constant.Comment: 19 pages, 13 figure
On two-dimensional quasitopological field theories
We study a class of lattice field theories in two dimensions that includes
gauge theories. We show that in these theories it is possible to implement a
broader notion of local symmetry, based on semi-simple Hopf algebras. A
character expansion is developed for the quasitopological field theories, and
partition functions are calculated with this tool. Expected values of
generalized Wilson loops are defined and studied with the character expansion.Comment: 17 pages, 6 figure