986 research outputs found
Differential Calculus on Quantum Spaces and Quantum Groups
A review of recent developments in the quantum differential calculus. The
quantum group is treated by considering it as a particular quantum
space. Functions on are defined as a subclass of functions on
. The case of is also briefly considered. These notes cover
part of a lecture given at the XIX International Conference on Group Theoretic
Methods in Physics, Salamanca, Spain 1992.Comment: 23 page
Non-Abelian Anomalies and Effective Actions for a Homogeneous Space
We consider the problem of constructing the fully gauged effective action in
-dimensional space-time for Nambu-Goldstone bosons valued in a homogeneous
space , with the requirement that the action be a solution of the
anomalous Ward identity and be invariant under the gauge transformations of
. We show that this can be done whenever the homotopy group
is trivial, is reductive and is embedded in so as to be anomaly
free, in particular if is an anomaly safe group. We construct the necessary
generalization of the Bardeen counterterm and give explicit forms for the
anomaly and the effective action. When is a symmetric space the
counterterm and the anomaly decompose into a parity even and a parity odd part.
In this case, for the parity even part of the action, one does not need the
anomaly free embedding of .Comment: revise
Reality in the Differential Calculus on q-euclidean Spaces
The nonlinear reality structure of the derivatives and the differentials for
the euclidean q-spaces are found. A real Laplacian is constructed and reality
properties of the exterior derivative are given.Comment: 10 page
Cartan Calculus on Quantum Lie Algebras
A generalization of the differential geometry of forms and vector fields to
the case of quantum Lie algebras is given. In an abstract formulation that
incorporates many existing examples of differential geometry on quantum spaces
we combine an exterior derivative, inner derivations, Lie derivatives, forms
and functions all into one big algebra, the ``Cartan Calculus''. (This is an
extended version of a talk presented by P. Schupp at the XXII
International Conference on Differential Geometric Methods in Theoretical
Physics, Ixtapa, Mexico, September 1993)Comment: 15 pages in LaTeX, LBL-34833 and UCB-PTH-93/3
Holomorphy, Minimal Homotopy and the 4D, N = 1 Supersymmetric Bardeen-Gross-Jackiw Anomaly
By use of a special homotopy operator, we present an explicit, closed-form
and simple expression for the left-right Bardeen-Gross-Jackiw anomalies
described as the proper superspace integral of a superfunction.Comment: 16 pp, LaTeX, Replacement includes addition comment on WZNW term and
one new referenc
Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
The vector fields of the quantum Lie algebra are described for the quantum
groups and as pseudodifferential operators on the
linear quantum spaces covariant under the corresponding quantum group. Their
expressions are simple and compact. It is pointed out that these vector fields
satisfy certain characteristic polynomial identities. The real forms
and are discussed in detail.Comment: 16 pages, Latex, no figures, to appear in the Proceedings of the XX
International Conference on Group Theory Methods in Physics, Toyonaka, Japan
(1994
Some remarks on unilateral matrix equations
We briefly review the results of our paper hep-th/0009013: we study certain
perturbative solutions of left-unilateral matrix equations. These are algebraic
equations where the coefficients and the unknown are square matrices of the
same order, or, more abstractly, elements of an associative, but possibly
noncommutative algebra, and all coefficients are on the left. Recently such
equations have appeared in a discussion of generalized Born-Infeld theories. In
particular, two equations, their perturbative solutions and the relation
between them are studied, applying a unified approach based on the generalized
Bezout theorem for matrix polynomials.Comment: latex, 6 pages, 1 figure, talk given at the euroconference "Brane New
World and Noncommutative Geometry", Villa Gualino, Torino, Italy, Oct 2-7,
200
- …