The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
We describe a noncommutative differential calculus, introduced in [1], which generalizes the differential calculus of differential forms of E. Cartan. We show that besides the classical (commutative) situation, this differential calculus is well suited to deal with ordinary quantum mechanics. That is quantum mechanics falls in the framework of a noncommutative symplectic geometry. We then introduce...
Tensor operators acting on model spaces for the quantum group SUq(n) are defined (“q-tensor operators”) and the fundamental theorem for q-tensor operators (a generalization to non-commutative co-products of the WignerEckart theorem) is proved. Examples from SUq(2) are discussed.
An explicit representation is constructed, starting with the operator algebra corresponding to the Coulomb gas representation of conformal field theories. By “quantizing” the uniformization theory of Riemann surfaces, the geometric interpretation of such a representation is obtained.
We explain the physical meaning of some recent results in category theory: Associated to any topological quantum field theory (in the sense of a functor) is a quasiquantum group of internal symmetries. Associated to any algebraic quantum field theory (where there is no functor) is a braided group. We also mention some joint work relating Chern-Simons theory to quantum mechanics in a bounded domain.
This talk reviews the basic definitions of Lie and Poisson groupoids and then proposes Lie Hopf Algebroids as a possible definition for “Quantum Groupoids” — objects which generalize quantum groups on the one hand, and have Poisson groupoids as their classical limits, on the other.
We give a review of our recent results concerning a new class of infinite-dimensional Lie algebras — the generalizations of Z-graded contragredient Lie algebras with a, generally speaking, infinite-dimensional Cartan subalgebra and a contiguous set of roots (a manifold or a more general space, for example with a measure). We call such algebras “continuum Lie algebras”. Special examples of these algebras...
We analyse the sl2 affine Toda field theory introduced elsewhere. In particular we study the chiral splitting of the theory and the relevant Drinfeld-Sokolov equations. We exhibit the chiral exchange algebra and the conformal properties of objects involved.
The BRS cohomology of Super-Yang-Mills coupled to chiral matter has non-trivial BRS cohomology, which leads to the conjecture that the local gauge-invariant and supersymmetric composite operators have anomalies in their renormalization. Since these operators are interpolating operators for bound states which are gauge-invariant and which ought naively to fall into supersymmetry multiplets, it follows...
We give a geometric description of some representations of the semidirect sum of the Virasoro and Kac-Moody algebras in terms of line bundles over the moduli stacks of stable vector bundles over smooth Riemann surfaces.
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.