338 research outputs found
The Master Field for the Half-Planar Approximation for Large Matrix Models and Boltzmann Field Theory
In this talk results of study in various dimensions of the Boltzmann master
field for a subclass of planar diagrams, so called half-planar diagrams, found
in the recent work by Accardi, Volovich and one of us (I.A.) are presented.Comment: Contr. Proc. Buckow Symposium (1995); 6 pages, LATEX uses
twoside.sty, fleqn.sty, espcrc2.sty, emlines.sty, bezier.st
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
We study one- and two-soliton solutions of noncommutative Chern-Simons theory
coupled to a nonrelativistic or a relativistic scalar field. In the
nonrelativistic case, we find a tower of new stationary time-dependent
solutions, all with the same charge density, but with increasing energies. The
dynamics of these solitons cannot be studied using traditional moduli space
techniques, but we do find a nontrivial symplectic form on the phase space
indicating that the moduli space is not flat. In the relativistic case we find
the metric on the two soliton moduli space.Comment: 22 pages, 2 figures, JHEP3 style. v2: This paper is a thoroughly
revised version. We thank P.A. Horvathy, L. Martina and P.C. Stichel for
illuminating comments that led us to reconsider some of our previously
reported results; see note added at the end of the paper. v3:
Acknowledgements adde
Noncommutative gravity: fuzzy sphere and others
Gravity on noncommutative analogues of compact spaces can give a finite mode
truncation of ordinary commutative gravity. We obtain the actions for gravity
on the noncommutative two-sphere and on the noncommutative in
terms of finite dimensional -matrices. The commutative large
limit is also discussed.Comment: LaTeX, 13 pages, section on CP^2 added + minor change
Aspects of Open-Closed Duality in a Background B-Field II
It was shown in [hep-th/0503009], in the context of bosonic theory that the
IR singular terms that arise as a result of integrating out high momentum modes
in nonplanar diagrams of noncommutative gauge theory can be recovered from low
lying tree-level closed string exchanges. This follows as a natural consequence
of world-sheet open-closed string duality. Here using the same setup we study
the phenomenon for noncommutative gauge theory realised on a
fractional brane localised at the fixed point of . The IR
singularities from the massless closed string exchanges are exactly equal to
those coming from one-loop gauge theory. This is as a result of cancellation of
all contributions from the massive modes.Comment: 27 pages, 1 figure, references added, typos correcte
The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection
On the fuzzy sphere, no state saturates simultaneously all the Heisenberg
uncertainties. We propose a weaker uncertainty for which this holds. The family
of states so obtained is physically motivated because it encodes information
about positions in this fuzzy context. In particular, these states realize in a
natural way a deformation of the stereographic projection. Surprisingly, in the
large limit, they reproduce some properties of the ordinary coherent states
on the non commutative plane.Comment: 18 pages, Latex. Minor changes in notations. Version to appear in
JHE
Spectrum of Schroedinger field in a noncommutative magnetic monopole
The energy spectrum of a nonrelativistic particle on a noncommutative sphere
in the presence of a magnetic monopole field is calculated. The system is
treated in the field theory language, in which the one-particle sector of a
charged Schroedinger field coupled to a noncommutative U(1) gauge field is
identified. It is shown that the Hamiltonian is essentially the angular
momentum squared of the particle, but with a nontrivial scaling factor
appearing, in agreement with the first-quantized canonical treatment of the
problem. Monopole quantization is recovered and identified as the quantization
of a commutative Seiberg-Witten mapped monopole field.Comment: 16 pages; references adde
Noncommutative Quantum Mechanics and rotating frames
We study the effect of noncommutativity of space on the physics of a quantum
interferometer located in a rotating disk in a gauge field background. To this
end, we develop a path-integral approach which allows defining an effective
action from which relevant physical quantities can be computed as in the usual
commutative case. For the specific case of a constant magnetic field, we are
able to compute, exactly, the noncommutative Lagrangian and the associated
shift on the interference pattern for any value of .Comment: 17 pages, presentation improved, references added. To appear in
Physical Review
Noncommutative massive Thirring model in three-dimensional spacetime
We evaluate the noncommutative Chern-Simons action induced by fermions
interacting with an Abelian gauge field in a noncommutative massive Thirring
model in (2+1)-dimensional spacetime. This calculation is performed in the
Dirac and Majorana representations. We observe that in Majorana representation
when goes to zero we do not have induced Chern-Simons term in the
dimensional regularization scheme.Comment: Accepted to Phys. Rev. D; 9 pages, Revtex4, no figures, references
added, minor improvements, Eq.31 correcte
Fredholm Determinants, Differential Equations and Matrix Models
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to
Fredholm determinants of integral operators with kernel of the form (phi(x)
psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm
determinants of integral operators having kernel of this form and where the
underlying set is a union of open intervals. The emphasis is on the
determinants thought of as functions of the end-points of these intervals. We
show that these Fredholm determinants with kernels of the general form
described above are expressible in terms of solutions of systems of PDE's as
long as phi and psi satisfy a certain type of differentiation formula. There is
also an exponential variant of this analysis which includes the circular
ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only
the abstract and decreases length of typeset versio
Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle
A covariant quantization method is developed for the off-shell superparticle
in 10 dimensions. On-shell it is consistent with lightcone quantization, while
off-shell it gives a noncommutative superspace that realizes non-linearly a
hidden 11-dimensional super Poincare symmetry. The non-linear commutation rules
are then used to construct the supersymmetric generalization of the covariant
Moyal star product in noncommutative superspace. As one of the possible
applications, we propose this new product as the star product in supersymmetric
string field theory. Furthermore, the formalism introduces new techniques and
concepts in noncommutative (super)geometry.Comment: 17 pages, LaTe
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