Search results for "Current algebra"
showing 10 items of 22 documents
The enveloping algebra of the Lie superalgebra osp(1,2)
1990
International audience
The new results on lattice deformation of current algebra
2008
The topic “Quantum Integrable Models” was reviewed in the literature and presented to the conferences and schools many times. Only the reports of our own have been done on quite a few occasions (see, e.g., [1], [2]). So here we shall try to present a fresh approach to the description of the ingredients of construction of integrable models. It has gradually evolved in the process of our joint work. Whereas our goal was the Sugawara construction for the lattice affine algebra (known now as the St.Petersburg algebra), (see, e.g., [1]), some technical developments happen to be new and useful for the already developed subjects. Here we shall underline this development.
Current Algebras as Hilbert Space Operator Cocycles
1994
Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.
Structure of Kac-Moody groups
2008
For a phys ic i s t , a Kac-Moody algebra is the current algebra of a quantum f i e l d theory model in I + I space-time dimensions with an in terna l symmetry group G [ I ] . A More p rec ise ly , l e t ~ be the Lie algebra of G . The Kac-Moody algebra g is a one-dimensional central extension of the loop algebra Map(S I , g ) . I f f l ' f2 C Map(S I ,~ ) , then the commutator is defined point -wise,
Effective-Lagrangian formulation of generalized vector dominance. II
1975
As in a preceding paper we generalize the Lagrangian of Lee and Zumino to include several mutually interacting vector mesons. The treatment is more general in the sense that all possible interactions between the vector mesons, compatible with the field-current proportionality relations, are now discussed. It is moreover demonstrated that also the fields corresponding to the physical vector mesons satisfy a field-current proportionality relation of exactly the same form. Comparison of the different schemes and their implications for the magnetic moments of the vector mesons are discussed.
Algebras of pseudodifferential operators on complete manifolds
2003
In several influential works, Melrose has studied examples of non-compact manifolds M 0 M_0 whose large scale geometry is described by a Lie algebra of vector fields V ⊂ Γ ( M ; T M ) \mathcal V \subset \Gamma (M;TM) on a compactification of M 0 M_0 to a manifold with corners M M . The geometry of these manifolds—called “manifolds with a Lie structure at infinity”—was studied from an axiomatic point of view in a previous paper of ours. In this paper, we define and study an algebra Ψ 1 , 0 , V ∞ ( M 0 ) \Psi _{1,0,\mathcal V}^\infty (M_0) of pseudodifferential operators canonically associated to a manifold M 0 M_0 with a Lie structure at infinity V ⊂ Γ ( M ; T M ) \mathcal V \subset \Gamma (…
The Virasoro Algebra
1989
In this chapter we shall study the Lie algebra Vect S1 of vector fields on a circle and some of its generalizations. The Lie algebra Vect S1 has a central extension, the Virasoro algebra. The representation theory of the Virasoro algebra is closely related to the representation theory of affine Lie algebras. In fact, through the Sugawara construction, to be defined below, a highest weight representation of an affine Lie algebra carries always a highest weight representation of the Virasoro algebra. All the irreducible highest weight representations of the Virasoro algebra are known and they can be exponentiated to representations of associated infinite-dimensional Lie groups. The representa…
The Bohm-Aharonov effect: A seven-dimensional structural group
1996
We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys.1 (1976), 155–163.
On a relation between massive Yang-Mills theories and dual string models
1983
The relations between mass terms in Yang-Mills theories, projective representations of the group of gauge transformations, boundary conditions on vector potentials and Schwinger terms in local charge algebra commutation relations are discussed. The commutation relations (with Schwinger terms) are similar to the current algebra commutation relations of the SU(N) extended dual string model.
Abelian current algebra and the Virasoro algebra on the lattice
1993
We describe how a natural lattice analogue of the abelian current algebra combined with free discrete time dynamics gives rise to the lattice Virasoro algebra and corresponding hierarchy of conservation laws.