176 research outputs found
Two Dimensional Fractional Supersymmetry from the Quantum Poincare Group at Roots of Unity
A group theoretical understanding of the two dimensional fractional
supersymmetry is given in terms of the quantum Poincare group at roots of
unity. The fractional supersymmetry algebra and the quantum group dual to it
are presented and the pseudo-unitary, irreducible representations of them are
obtained. The matrix elements of these representations are explicitly
constructed.Comment: 10 pages. Some misprints are corrected. To appear in J. Phys.
On the question of deconfinement in noncommutative Schwinger Model
The 1+1 dimensional bosonised Schwinger model with a generalized gauge
invariant regularisation has been studied in a noncommutative scenario to
investigate the fate of the transition from confinement to deconfinement
observed in the commutative setting. We show that though the fuzziness of space
time introduces new features in the confinement scenario, it does not affect
the deconfining limit.Comment: 4 pages, revTe
N=1/2 Supersymmetric gauge theory in noncommutative space
A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory
in noncommutative space is studied. We show that at one loop
UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative
and non-anticommutative superspace is employed to obtain an action in terms of
commuting fields at first order in the noncommutativity parameter tetha. This
leads to abelian and non-abelian gauge theories whose supersymmetry
transformations are local and non-local, respectively.Comment: One reference added, published versio
Dirac Fermions in Inhomogeneous Magnetic Field
We study a confined system of Dirac fermions in the presence of inhomogeneous
magnetic field. Splitting the system into different regions, we determine their
corresponding energy spectrum solutions. We underline their physical properties
by considering the conservation energy where some interesting relations are
obtained. These are used to discuss the reflexion and transmission coefficients
for Dirac fermions and check the probability condition for different cases. We
generalize the obtained results to a system with gap and make some analysis.
After evaluating the current-carrying states, we analyze the Klein paradox and
report interesting discussions.Comment: 28 pages, 15 figures. Version to appear in JP
Duals of noncommutative supersymmetric U(1) gauge theory
Parent actions for component fields are utilized to derive the dual of
supersymmetric U(1) gauge theory in 4 dimensions. Generalization of the
Seiberg-Witten map to the component fields of noncommutative supersymmetric
U(1) gauge theory is analyzed. Through this transformation we proposed parent
actions for noncommutative supersymmetric U(1) gauge theory as generalization
of the ordinary case.Duals of noncommutative supersymmetric U(1) gauge theory
are obtained. Duality symmetry under the interchange of fields with duals
accompanied by the replacement of the noncommutativity parameter
\Theta_{\mu\nu} with \tilde{\Theta}_{\mu \nu} =
\epsilon_{\mu\nu\rho\sigma}\Theta^{\rho\sigma} of the non--supersymmetric case
is broken at the level of actions. We proposed a noncommutative parent action
for the component fields which generates actions possessing this duality
symmetry.Comment: Typos corrected. Version which will appear in JHE
Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic
dipole moments interacting with external electric and magnetic fields in
noncommutative coordinates is obtained. Noncommutativity of space is interposed
in terms of a semiclassical constrained Hamiltonian system. The relation
between the quantum phase acquired by a particle interacting with an
electromagnetic field and the (semi)classical force acting on the system is
examined and generalized to establish a formulation of the quantum phases in
noncommutative coordinates. The general formalism is applied to physical
systems yielding the Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and
Anandan phases in noncommutative coordinates. Bounds for the noncommutativity
parameter theta are derived comparing the deformed phases with the experimental
data on the Aharonov-Bohm and Aharonov-Casher phases.Comment: Some clarifications, a new bound on theta and references are adde
Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories
We show that noncommuting electric fields occur naturally in
-expanded noncommutative gauge theories. Using this noncommutativity,
which is field dependent, and a hamiltonian generalisation of the
Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian
formulations of these theories, is established. A comparison of results in
different descriptions shows that this generalised map acts as canonical
transformation in the physical subspace only. Finally, we apply the hamiltonian
formulation to derive the gauge symmetries of the action.Comment: 16 pages, LaTex, considerably expanded version with a new section on
`Gauge symmetries'; To appear in Phys. Rev.
Two Coupled Harmonic Oscillators on Non-commutative Plane
We investigate a system of two coupled harmonic oscillators on the
non-commutative plane \RR^2_{\theta} by requiring that the spatial coordinates
do not commute. We show that the system can be diagonalized by a suitable
transformation, i.e. a rotation with a mixing angle \alpha. The obtained
eigenstates as well as the eigenvalues depend on the non-commutativity
parameter \theta. Focusing on the ground state wave function before the
transformation, we calculate the density matrix \rho_0(\theta) and find that
its traces {\rm Tr}(\rho_{0}(\theta)) and {\rm Tr}(\rho_0^2(\theta)) are not
affected by the non-commutativity. Evaluating the Wigner function on
\RR^2_{\theta} confirms this. The uncertainty relation is explicitly determined
and found to depend on \theta. For small values of \theta, the relation is
shifted by a \theta^2 term, which can be interpreted as a quantum correction.
The calculated entropy does not change with respect to the normal case. We
consider the limits \alpha=1 and \alpha={\pi\over 2}. In first case, by
identifying \theta to the squared magnetic length, one can recover basic
features of the Hall system.Comment: 15 pages, 1 figur
The -value Equation and Wigner Distributions in Noncommutative Heisenberg algebras
We consider the quantum mechanical equivalence of the Seiberg-Witten map in
the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order
to construct a quantum mechanics over noncommutative Heisenberg algebras. The
formalism is then applied to the exactly soluble Landau and harmonic oscillator
problems in the 2-dimensional noncommutative phase-space plane, in order to
derive their correct energy spectra and corresponding Wigner distributions. We
compare our results with others that have previously appeared in the
literature.Comment: 19 page
- …