1,237 research outputs found
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
Lattices and Their Continuum Limits
We address the problem of the continuum limit for a system of Hausdorff
lattices (namely lattices of isolated points) approximating a topological space
. The correct framework is that of projective systems. The projective limit
is a universal space from which can be recovered as a quotient. We dualize
the construction to approximate the algebra of continuous
functions on . In a companion paper we shall extend this analysis to systems
of noncommutative lattices (non Hausdorff lattices).Comment: 11 pages, 1 Figure included in the LaTeX Source New version, minor
modifications (typos corrected) and a correction in the list of author
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
Quasi-Topological Field Theories in Two Dimensions as Soluble Models
We study a class of lattice field theories in two dimensions that includes
gauge theories. Given a two dimensional orientable surface of genus , the
partition function is defined for a triangulation consisting of
triangles of area . The reason these models are called
quasi-topological is that depends on , and but not on the
details of the triangulation. They are also soluble in the sense that the
computation of their partition functions can be reduced to a soluble one
dimensional problem. We show that the continuum limit is well defined if the
model approaches a topological field theory in the zero area limit, i.e.,
with finite . We also show that the universality classes of
such quasi-topological lattice field theories can be easily classified.
Yang-Mills and generalized Yang-Mills theories appear as particular examples of
such continuum limits.Comment: 23 pages, 16 figures, uses psbox.te
Endometriosis: A Rare Cause of Large Bowel Obstruction.
Large bowel obstruction can result in significant morbidity and mortality, especially in cases of acute complete obstruction. There are many possible causes, the most common in adults being colorectal cancer. Endometriosis is a benign disease, and the most affected extragenital location is the bowel, especially the rectosigmoid junction. However, transmural involvement and acute occlusion are very rare events. We report an exceptional case of acute large bowel obstruction as the initial presentation of endometriosis. The differential diagnosis of colorectal carcinoma may be challenging, and this case emphasizes the need to consider intestinal endometriosis in females at a fertile age presenting with gastrointestinal symptoms and an intestinal mass causing complete large bowel obstruction.info:eu-repo/semantics/publishedVersio
Topological low-temperature limit of Z(2) spin-gauge theory in three dimensions
We study Z(2) lattice gauge theory on triangulations of a compact 3-manifold.
We reformulate the theory algebraically, describing it in terms of the
structure constants of a bidimensional vector space H equipped with algebra and
coalgebra structures, and prove that in the low-temperature limit H reduces to
a Hopf Algebra, in which case the theory becomes equivalent to a topological
field theory. The degeneracy of the ground state is shown to be a topological
invariant. This fact is used to compute the zeroth- and first-order terms in
the low-temperature expansion of Z for arbitrary triangulations. In finite
temperatures, the algebraic reformulation gives rise to new duality relations
among classical spin models, related to changes of basis of H.Comment: 10 pages, no figure
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