67 research outputs found
Hopf Map and Quantization on Sphere
Quantization of a system constrained to move on a sphere is considered by
taking a square root of the ``on sphere condition''. We arrive at the fibre
bundle structure of the Hopf map in the cases of and . This
leads to more geometrical understanding of monopole and instanton gauge
structures that emerge in the course of quantization.Comment: 9 pages, LaTeX2e, uses amsmath.st
Inequivalent Quantization in the Skyrme Model
Quantum mechanics on manifolds is not unique and in general infinite number
of inequivalent quantizations can be considered. They are specified by the
induced spin and the induced gauge structures on the manifold. The
configuration space of collective mode in the Skyrme model can be identified
with and thus the quantization is not unique. This leads to the
different predictions for the physical observables.Comment: 16 pages, LaTeX2
Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere
Quantum mechanics on sphere is studied from the viewpoint that the
Berry's connection has to appear as a topological term in the effective action.
Furthermore we show that this term is the Chern-Simons term of gauge variables
that correspond to the extra degrees of freedom of the enlarged space.Comment: 12 pages, LaTeX2
On the symmetries of BF models and their relation with gravity
The perturbative finiteness of various topological models (e.g. BF models)
has its origin in an extra symmetry of the gauge-fixed action, the so-called
vector supersymmetry. Since an invariance of this type also exists for gravity
and since gravity is closely related to certain BF models, vector supersymmetry
should also be useful for tackling various aspects of quantum gravity. With
this motivation and goal in mind, we first extend vector supersymmetry of BF
models to generic manifolds by incorporating it into the BRST symmetry within
the Batalin-Vilkovisky framework. Thereafter, we address the relationship
between gravity and BF models, in particular for three-dimensional space-time.Comment: 29 page
Solitons of Sigma Model on Noncommutative Space as Solitons of Electron System
We study the relationship of soliton solutions for electron system with those
of the sigma model on the noncommutative space, working directly in the
operator formalism. We find that some soliton solutions of the sigma model are
also the solitons of the electron system and are classified by the same
topological numbers.Comment: 12 pages, LaTeX2e, improvements to discussions, Version to be
published in JHE
Lost equivalence of nonlinear sigma and models on noncommutative space
We show that the equivalence of nonlinear sigma and models which is
valid on the commutative space is broken on the noncommutative space. This
conclusion is arrived at through investigation of new BPS solitons that do not
exist in the commutative limit.Comment: 17 pages, LaTeX2
New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model
Investigating the solitons in the non-commutative model, we have
found a new set of BPS solitons which does not have counterparts in the
commutative model.Comment: 8 pages, LaTeX2e, references added, improvements to discussions,
Version to be published in JHE
Symmetries of topological field theories in the BV-framework
Topological field theories of Schwarz-type generally admit symmetries whose
algebra does not close off-shell, e.g. the basic symmetries of BF models or
vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this
symmetry being at the origin of the perturbative finiteness of the theory). We
present a detailed discussion of all these symmetries within the algebraic
approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general
algebraic construction of topological models of both Schwarz- and Witten-type.Comment: 30 page
A Superspace Formulation of The BV Action for Higher Derivative Theories
We first analyze the anti-BRST and double BRST structures of a certain higher
derivative theory that has been known to possess BRST symmetry associated with
its higher derivative structure. We discuss the invariance of this theory under
shift symmetry in the Batalin Vilkovisky (BV) formalism. We show that the
action for this theory can be written in a manifestly extended BRST invariant
manner in superspace formalism using one Grassmann coordinate.
It can also be written in a manifestly extended BRST invariant manner and
on-shell manifestly extended anti-BRST invariant manner in superspace formalism
using two Grassmann coordinates.Comment: accepted for publication in EPJ
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