90 research outputs found
Fractional quantum Hall effect on the two-sphere: a matrix model proposal
We present a Chern-Simons matrix model describing the fractional quantum Hall
effect on the two-sphere. We demonstrate the equivalence of our proposal to
particular restrictions of the Calogero-Sutherland model, reproduce the quantum
states and filling fraction and show the compatibility of our result with the
Haldane spherical wavefunctions.Comment: 26 pages, LaTeX, no figures, references adde
Non-commutative Euclidean structures in compact spaces
Based on results for real deformation parameter q we introduce a compact non-
commutative structure covariant under the quantum group SOq(3) for q being a
root of unity. To match the algebra of the q-deformed operators with necesarry
conjugation properties it is helpful to define a module over the algebra
genera- ted by the powers of q. In a representation where X is diagonal we show
how P can be calculated. To manifest some typical properties an example of a
one-di- mensional q-deformed Heisenberg algebra is also considered and compared
with non-compact case.Comment: Changed conten
Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry
The non commutative geometry is a possible framework to regularize Quantum
Field Theory in a nonperturbative way. This idea is an extension of the lattice
approximation by non commutativity that allows to preserve symmetries. The
supersymmetric version is also studied and more precisely in the case of the
Schwinger model on supersphere [14]. This paper is a generalization of this
latter work to more general gauge groups
Hilbert Space Representation of an Algebra of Observables for q-Deformed Relativistic Quantum Mechanics
Using a representation of the q-deformed Lorentz algebra as differential
operators on quantum Minkowski space, we define an algebra of observables for a
q-deformed relativistic quantum mechanics with spin zero. We construct a
Hilbert space representation of this algebra in which the square of the mass is diagonal.Comment: 13 pages, LMU-TPW 94-
Quantum cosmology of 5D non-compactified Kaluza-Klein theory
We study the quantum cosmology of a five dimensional non-compactified
Kaluza-Klein theory where the 4D metric depends on the fifth coordinate,
. This model is effectively equivalent to a 4D non-minimally
coupled dilaton field in addition to matter generated on hypersurfaces
l=constant by the extra coordinate dependence in the four-dimensional metric.
We show that the Vilenkin wave function of the universe is more convenient for
this model as it predicts a new-born 4D universe on the constant
hypersurface.Comment: 14 pages, LaTe
The N=1 superstring as a topological field theory
By "untwisting" the construction of Berkovits and Vafa, one can see that the
N=1 superstring contains a topological twisted N=2 algebra, with central charge
c^ = 2. We discuss to what extent the superstring is actually a topological
theory.Comment: 8 Pages (LaTeX). TAUP-2155-9
Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
Covariant differential calculi and exterior algebras on quantum homogeneous
spaces endowed with the action of inhomogeneous quantum groups are classified.
In the case of quantum Minkowski spaces they have the same dimensions as in the
classical case. Formal solutions of the corresponding Klein--Gordon and Dirac
equations are found. The Fock space construction is sketched.Comment: 21 pages, LaTeX file, minor change
Operator identities in q-deformed Clifford analysis
In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied
Examples of q-regularization
An Introduction to Hopf algebras as a tool for the regularization of relavent
quantities in quantum field theory is given. We deform algebraic spaces by
introducing q as a regulator of a non-commutative and non-cocommutative Hopf
algebra. Relevant quantities are finite provided q\neq 1 and diverge in the
limit q\rightarrow 1. We discuss q-regularization on different q-deformed
spaces for \lambda\phi^4 theory as example to illustrate the idea.Comment: 17 pages, LaTex, to be published in IJTP 1995.1
Realization of within the differntial algebra on
We realize the Hopf algebra as an algebra of differential
operators on the quantum Euclidean space . The generators are
suitable q-deformed analogs of the angular momentum components on ordinary
. The algebra of functions on
splits into a direct sum of irreducible vector representations of
; the latter are explicitly constructed as highest weight
representations.Comment: 26 pages, 1 figur
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