Concrete Fock representations of Mickelsson-Faddeev-like algebras
نویسنده
چکیده
The Mickelsson-Faddeev (MF) algebra can naturally be embedded in a non-Lie algebra, which suggests that it has no Fock representations. The difficulties are due to the inhomogeneous term in the connection’s transformation law. Omitting this term yields a “classical MF algebra”, which has other abelian extensions that do possess Fock modules. I explicitly construct such modules and the intertwining action of the higher-dimensional Virasoro algebra.
منابع مشابه
Extensions of diffeomorphism and current algebras
Dzhumadil’daev has classified all tensor module extensions of diff(N), the diffeomorphism algebra in N dimensions, and its subalgebras of divergence free, Hamiltonian, and contact vector fields. I review his results using explicit tensor notation. All of his generic cocycles are limits of trivial cocycles, and many arise from the Mickelsson-Faddeev algebra for gl(N). Then his results are extend...
متن کاملChern - Simons Forms , Mickelsson - Faddeev Algebras and the P - Branes
In string theory, nilpotence of the BRS operator δ for the string functional relates the Chern-Simons term in the gauge-invariant antisymmetric tensor field strength to the central term in the Kac-Moody algebra. We generalize these ideas to p-branes with odd p and find that the Kac-Moody algebra for the string becomes the Mickelsson-Faddeev algebra for the p-brane.
متن کاملHopf Structure and Green Ansatz of Deformed Parastatistics Algebras
Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Gree...
متن کاملWhy the Mickelsson-faddeev Algebra Lacks Unitary Representations
A simple plausibility argument is given. Let g be a finite-dimensional Lie algebra with generators J a and structure constants f ab c. The brackets are given by [J a , J b ] = f ab c J c. Denote the symmetric Killing metric (proportional to the quadratic Casimir operator) by δ ab = tr J a J b , and let the totally symmetric third Casimir operator be d abc = tr {J a , J b }J c .
متن کاملar X iv : h ep - t h / 03 03 18 7 v 1 2 1 M ar 2 00 3 March 2003 Reflection – Transmission Algebras
Inspired by factorized scattering from delta–type impurities in (1+1)-dimensional space-time, we propose and analyse a generalization of the Zamolodchikov–Faddeev algebra. Distinguished elements of the new algebra, called reflection and transmission generators, encode the particle–impurity interactions. We describe in detail the underlying algebraic structure. The relative Fock representations ...
متن کامل