21 research outputs found
Hamiltonian formulation of nonAbelian noncommutative gauge theories
We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge
theory, considering with some detail the algebraic structure of the
noncommutative symmetry group. The first class constraints and Hamiltonian are
obtained and their algebra derived, as well as the form of the gauge invariance
they impose on the first order action.Comment: enlarged version, 7 pages, RevTe
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
Isotropic representation of noncommutative 2D harmonic oscillator
We show that 2D noncommutative harmonic oscillator has an isotropic
representation in terms of commutative coordinates. The noncommutativity in the
new mode, induces energy level splitting, and is equivalent to an external
magnetic field effect. The equivalence of the spectra of the isotropic and
anisotropic representation is traced back to the existence of SU(2) invariance
of the noncommutative model.Comment: 15 pages, RevTex4, no figures; article format, improved version of
the previous paper; new references and aknowledgements adde
Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
Classically, the dual under the Seiberg-Witten map of noncommutative U(N),
{\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge
symmetry whose fields carry, however, a \theta-deformed nonlinear realisation
of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter
theory we work out at one-loop and first order in the noncommutative parameter
matrix \theta^{\mu\nu} the UV divergent part of its effective action in the
background-field gauge, and, for N>=2, we show that for finite values of N the
gauge sector fails to be renormalisable; however, in the large N limit the full
theory is renormalisable, in keeping with the expectations raised by the
quantum behaviour of the theory's noncommutative classical dual. We also obtain
--for N>=3, the case with N=2 being trivial-- the UV divergent part of the
effective action of the SU(N) noncommutative theory in the enveloping-algebra
formalism that is obtained from the previous ordinary U(N) theory by removing
the U(1) degrees of freedom. This noncommutative SU(N) theory is also
renormalisable.Comment: 33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3:
New types of field redefinitions were considered, which make the large N U(N)
and the SU(N) theories renormalisable. The conclusions for U(N) with finite N
remain unchanged. Version 4: Corrected mistyped equations, minor revision
The Hamiltonian BRST quantization of a noncommutative nonabelian gauge theory and its Seiberg-Witten map
We consider the Hamiltonian BRST quantization of a noncommutative non abelian
gauge theory. The Seiberg-Witten map of all phase-space variables, including
multipliers, ghosts and their momenta, is given in first order in the
noncommutative parameter . We show that there exists a complete
consistence between the gauge structures of the original and of the mapped
theories, derived in a canonical way, once we appropriately choose the map
solutions.Comment: 10 pages, Latex. Address adde
The topological AC effect on noncommutative phase space
The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is
studied. Instead of using the star product method, we use a generalization of
Bopp's shift method. After solving the Dirac equations both on noncommutative
space and noncommutative phase space by the new method, we obtain the
corrections to AC phase on NC space and NC phase space respectively.Comment: 8 pages, Latex fil
Seiberg-Witten Map for Superfields on Canonically Deformed N=1, d=4 Superspace
In this paper we construct Seiberg-Witten maps for superfields on canonically
deformed N=1, d=4 Minkowski and Euclidean superspace. On Minkowski superspace
we show that the Seiberg-Witten map is not compatible with locality,
(anti)chirality and supersymmetry at the same time. On Euclidean superspace we
show that there exists a local, chiral and supersymmetric Seiberg-Witten map
for chiral superfields if we take the noncommutativity parameter to be
selfdual, and a local, antichiral and supersymmetric Seiberg-Witten map for
antichiral superfields if we take the noncommutativity parameter to be
antiselfdual, respectively.Comment: 24 pages, LaTeX; typos corrected, two comments adde
Noncommutative Quantum Mechanics and Seiberg-Witten Map
In order to overcome ambiguity problem on identification of mathematical
objects in noncommutative theory with physical observables, quantum mechanical
system coupled to the NC U(1) gauge field in the noncommutative space is
reformulated by making use of the unitarized Seiberg-Witten map, and applied to
the Aharonov-Bohm and Hall effects of the NC U(1) gauge field. Retaining terms
only up to linear order in the NC parameter \theta, we find that the AB
topological phase and the Hall conductivity have both the same formulas as
those of the ordinary commutative space with no \theta-dependence.Comment: 7 pages, no figures, uses revtex4; 8 pages, conclusion changed,
Appendix adde
Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
In the present contribution we investigate the Landau analog energy
quantization for neutral particles, that possesses a nonzero permanent magnetic
and electric dipole moments, in the presence of an homogeneous electric and
magnetic external fields in the context of the noncommutative quantum
mechanics. Also, we analyze the Landau--Aharonov--Casher and
Landau--He--McKellar--Wilkens quantization due to noncommutative quantum
dynamics of magnetic and electric dipoles in the presence of an external
electric and magnetic fields and the energy spectrum and the eigenfunctions are
obtained. Furthermore, we have analyzed Landau quantization analogs in the
noncommutative phase space, and we obtain also the energy spectrum and the
eigenfunctions in this context.Comment: 20 pages, references adde
Time-Space Noncommutativity in Gravitational Quantum Well scenario
A novel approach to the analysis of the gravitational well problem from a
second quantised description has been discussed. The second quantised formalism
enables us to study the effect of time space noncommutativity in the
gravitational well scenario which is hitherto unavailable in the literature.
The corresponding first quantized theory reveals a leading order perturbation
term of noncommutative origin. Latest experimental findings are used to
estimate an upper bound on the time--space noncommutative parameter. Our
results are found to be consistent with the order of magnitude estimations of
other NC parameters reported earlier.Comment: 7 pages, revTe