1,233 research outputs found
Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term
We study the nonrelativistic nonlinear sigma model with Hopf term in this
paper. This is an important issue beacuse of its relation to the currently
interesting studies in skyrmions in quantum Hall systems. We perform the
Hamiltonian analysis of this system in variables. When the coefficient
of the Hopf term becomes zero we get the Landau-Lifshitz description of the
ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian
analysis. The spin algebra is modified giving a new structure and
interpretation to the system. We point out momentum and angular momentum
generators and new features they bring in to the system.Comment: 16pages, Latex file, typos correcte
Fermionic edge states and new physics
We investigate the properties of the Dirac operator on manifolds with
boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact
counting of the number of edge states for boundaries with isometry of a sphere
is given. We show that the problem with the above boundary condition can be
mapped to one where the manifold is extended beyond the boundary and the
boundary condition is replaced by a delta function potential of suitable
strength. We also briefly highlight how the problem of the self-adjointness of
the operators in the presence of moving boundaries can be simplified by
suitable transformations which render the boundary fixed and modify the
Hamiltonian and the boundary condition to reflect the effect of moving
boundary.Comment: 24 pages, 3 figures. Title changed, additional material in the
Introduction section, the Application section and in the Discussion section
highlighting some recent work on singular potentials, several references
added. Conclusions remain unchanged. Version matches the version to appear in
PR
Beyond fuzzy spheres
We study polynomial deformations of the fuzzy sphere, specifically given by
the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the
Poisson structure on a surface in . We find that several
surfaces, differing by constants, are described by the Higgs algebra at the
fuzzy level. Some of these surfaces have a singularity and we overcome this by
quantizing this manifold using coherent states for this nonlinear algebra. This
is seen in the measure constructed from these coherent states. We also find the
star product for this non-commutative algebra as a first step in constructing
field theories on such fuzzy spaces.Comment: 9 pages, 3 Figures, Minor changes in the abstract have been made. The
manuscript has been modified for better clarity. A reference has also been
adde
Representations of Composite Braids and Invariants for Mutant Knots and Links in Chern-Simons Field Theories
We show that any of the new knot invariants obtained from Chern-Simons theory
based on an arbitrary non-abelian gauge group do not distinguish isotopically
inequivalent mutant knots and links. In an attempt to distinguish these knots
and links, we study Murakami (symmetrized version) -strand composite braids.
Salient features of the theory of such composite braids are presented.
Representations of generators for these braids are obtained by exploiting
properties of Hilbert spaces associated with the correlators of Wess-Zumino
conformal field theories. The -composite invariants for the knots are given
by the sum of elementary Chern-Simons invariants associated with the
irreducible representations in the product of representations (allowed by
the fusion rules of the corresponding Wess-Zumino conformal field theory)
placed on the individual strands of the composite braid. On the other hand,
composite invariants for links are given by a weighted sum of elementary
multicoloured Chern-Simons invariants. Some mutant links can be distinguished
through the composite invariants, but mutant knots do not share this property.
The results, though developed in detail within the framework of
Chern-Simons theory are valid for any other non-abelian gauge group.Comment: Latex, 25pages + 16 diagrams available on reques
Chirality of Knots and and Chern-Simons Theory
Upto ten crossing number, there are two knots, and whose
chirality is not detected by any of the known polynomials, namely, Jones
invariants and their two variable generalisations, HOMFLY and Kauffman
invariants. We show that the generalised knot invariants, obtained through
Chern-Simons topological field theory, which give the known polynomials
as special cases, are indeed sensitive to the chirality of these knots.Comment: 15 pages + 7 diagrams (available on request
Information from quantum blackhole physics
The study of BTZ blackhole physics and the cosmological horizon of 3D de
Sitter spaces are carried out in unified way using the connections to the Chern
Simons theory on three manifolds with boundary. The relations to CFT on the
boundary is exploited to construct exact partition functions and obtain
logarithmic corrections to Bekenstein formula in the asymptotic regime.
Comments are made on the dS/CFT correspondence frising from these studies.Comment: 11 pages; 1 figure(eps file);Talk presented at the conference
Space-time and Fundamental Interactions: Quantum Aspects'' in honour of A.P.
Balachandran's 65th birthday, Vietri sul Mare, Salerno, Italy 26th-31st May,
200
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