arXiv subjects

O. F. Dayi

Publications and source records attributed to O. F. Dayi.

34 records · Page 2Linked to original sources

arXiv2001

Hall Effect in Noncommutative Coordinates

We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov--Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θcan be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates.

hep-th↗

arXiv2001

Landau Diamagnetism in Noncommutative Space and the Nonextensive Thermodynamics of Tsallis

We consider the behavior of electrons in an external uniform magnetic field B where the space coordinates perpendicular to B are taken as noncommuting. This results in a generalization of standard thermodynamics. Calculating the susceptibility, we find that the usual Landau diamagnetism is modified. We also compute the susceptibility according to the nonextensive statistics of Tsallis for (1-q)<<1, in terms of the factorization approach. Two methods agree under certain conditions.

cond-mat.stat-mech↗

arXiv2000

Non-Abelian Fractional Supersymmetry in Two Dimensions

Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing $U_q(sl(2,\Rcc))$ at roots of unity. Its representations and the matrix elements are obtained. The dual of it is constructed and the corepresentations are studied. Moreover, a differential realization of the non-Abelian fractional supersymmetry generators is given in the generalized superspace defined by two commuting and two generalized Grassmann variables. An invariant action under the fractional supersymmetry transformations is given.

math.QA↗

arXiv1999

SL_q(2,R) at Roots of Unity

The quantum group SL_q(2,R) at roots of unity is introduced by means of duality pairings with the quantum algebra U_q(sl(2,R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this quantum group is given. Endowed with that some properties like unitarity and orthogonality of the irreducible representations are discussed.

math.QA↗

arXiv1999

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.

math.QA↗

arXiv1998

Hamiltonian Formulation of Jackiw--Pi 3-Dimensional Gauge Theories

A 3-dimensional non-abelian gauge theory was proposed by Jackiw and Pi to create mass for the gauge fields. However, the quadratic action obtained by switching off the non-abelian interactions possesses more gauge symmetries than the original one, causing some difficulties in quantization. Jackiw and Pi proposed another action by introducing new fields, whose gauge symmetries are consistent with the quadratic part. It is shown that all of these theories have the same number of physical degrees of freedom in the hamiltonian framework. Hence, as far as the physical states are considered there is no inconsistency. Nevertheless, perturbation expansion is still problematic. To cure this we propose to modify one of the constraints of the non-abelian theory without altering neither its canonical hamiltonian nor the number of physical states.

hep-th↗

arXiv1998

Quantum Hall Effect Wave Functions as Cyclic Representations of U_q(sl(2))

Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wave functions Ψ_{P/Q} possessing filling factors P/Q<1 where Q is odd and P, Q are relatively prime integers are classified in terms of U_q(sl(2)).

q-alg↗

arXiv1997

q-deformed Star Products and Moyal Brackets

The standard and anti-standard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called W_\infty. q-star products and q-Moyal brackets corresponding to these algebras are constructed. Some applications like defining q-classical mechanics and q-path integrals are discussed.

q-alg↗

arXiv1997

q-Schrodinger Equations for V=u^2+ 1/u^2 and Morse Potentials in terms of the q-canonical Transformation

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schrödinger equations for the Morse and the $V=u^2+1/u^2$ potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl_q(2) algebra is presented. By the virtue of the q-canonical transformation a q-deformed Schrödinger equation for the Morse potential is obtained from the q-deformed $V=u^2+ 1/u^2$ Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.

hep-th↗

arXiv1997

Consistent Interactions in terms of the Generalized Fields Method

The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method of solving the Batalin-Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to spin-1 gauge field in 3 and 4 dimensions, to free BF theory in 2-d and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological techniques.

hep-th↗

arXiv1995

$sl_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schrödinger equation for a Kepler like potential is obtained from the q-oscillator Schrödinger equation. Energy spectrum and the ground state wave function are calculated.

hep-th↗

arXiv1994

BV and BFV Formulation of a Gauge Theory of Quadratic Lie Algebras in 2-d and a Construction of W3 Topological Gravity

The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived from this solution in terms of the phase space variables by using the Noether procedure, and the one found due to the BFV-method are compared and found to coincide. $W_3$ algebra, formulated in terms of a continuous variable is emploied in the mentioned gauge theory to construct a $W_3$ topological gravity. Moreover, its gauge fixing is briefly discussed.

hep-th↗

arXiv1993

A General Solution of the BV-Master Equation and BRST Field Theories

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization.

hep-th↗

arXiv1993

BFV--BRST Analysis of the Classical and Quantum q-deformations of the sl(2) Algebra

BFV--BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the $q$-deformed algebra sl_q(2) are discussed. Moreover, deformation of the phase space without deforming the generators of sl(2) is considered. $\hbar$-q-deformation of the phase space is shown to yield the Witten's second deformation. To study the BFV--BRST cohomology problem when both the quantum phase space and the group are deformed, a two parameter deformation of sl(2) is proposed, and its BFV-BRST charge is given.

hep-th↗

arXiv1992

A General Solution of the Master Equation for a Class of First Order Systems

Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of ``odd time'', we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the interaction part satisfies some properties, it is possible to give the solution of the master equation in a very simple way. To clarify the general procedure we discuss its application to Yang-Mills theory, massive (abelian) theory in the Stueckelberg formalism, relativistic particle and to the self-interacting antisymmetric tensor field.

hep-th↗

arXiv1992

Solution of the Master Equation in Terms of the Odd Time Formulation

A systematic way of formulating the Batalin-Vilkovisky method of quantization was obtained in terms of the ``odd time'' formulation. We show that in a class of gauge theories it is possible to find an ``odd time lagrangian'' yielding, by a Legendre transformation, an ``odd time hamiltonian'' which is the minimal solution of the master equation. This constitutes a very simple method of finding the minimal solution of the master equation which is usually a tedious task. To clarify the general procedure we discussed its application to Yang-Mills theory, massive (abelian) theory in Stueckelberg formalism, relativistic particle and the self-interacting antisymmetric tensor field.

hep-th↗