115 research outputs found
(Non)renormalizability of the D-deformed Wess-Zumino model
We continue the analysis of the -deformed Wess-Zumino model which was
started in the previous paper. The model is defined by a deformation which is
non-hermitian and given in terms of the covariant derivatives . We
calculate one-loop divergences in the two-point, three-point and four-point
Green functions. We find that the divergences in the four-point function cannot
be absorbed and thus our model is not renormalizable. We discuss possibilities
to render the model renormalizable.Comment: 19 pages; version accepted for publication in Phys.Rev.D; new section
with the detailed discussion on renormalizabilty added and a special choice
of coupling constants which renders the model renormalizable analyze
Twisted Yangians and folded W-algebras
We show that the truncation of twisted Yangians are isomorphic to finite
W-algebras based on orthogonal or symplectic algebras. This isomorphism allows
us to classify all the finite dimensional irreducible representations of the
quoted W-algebras. We also give an R-matrix for these W-algebras, and determine
their center.Comment: LaTeX 2e Document, 22 page
Twisted Yangians of small rank
We study quantized enveloping algebras called twisted Yangians associated with the symmetric pairs of types CI, BDI, and DIII (in Cartan’s classification) when the rank is small. We establish isomorphisms between these twisted Yangians and the well known Olshanskii’s twisted Yangians of types AI and AII, and also with the Molev-Ragoucy reflection algebras associated with symmetric pairs of type AIII. We also construct isomorphisms with twisted Yangians in Drinfeld’s original presentation
Evaluation representations of quantum affine algebras at roots of unity
The purpose of this paper is to compute the Drinfel'd polynomials for two
types of evaluation representations of quantum affine algebras at roots of
unity and construct those representations as the submodules of evaluation
Schnizer modules. Moreover, we obtain the necessary and sufficient condition
for that the two types of evaluation representations are isomorphic to each
other
Lie-Poisson Deformation of the Poincar\'e Algebra
We find a one parameter family of quadratic Poisson structures on which satisfies the property {\it a)} that it is preserved
under the Lie-Poisson action of the Lorentz group, as well as {\it b)} that it
reduces to the standard Poincar\'e algebra for a particular limiting value of
the parameter. (The Lie-Poisson transformations reduce to canonical ones in
that limit, which we therefore refer to as the `canonical limit'.) Like with
the Poincar\'e algebra, our deformed Poincar\'e algebra has two Casimir
functions which we associate with `mass' and `spin'. We parametrize the
symplectic leaves of with space-time coordinates,
momenta and spin, thereby obtaining realizations of the deformed algebra for
the cases of a spinless and a spinning particle. The formalism can be applied
for finding a one parameter family of canonically inequivalent descriptions of
the photon.Comment: Latex file, 26 page
Classification of two and three dimensional Lie super-bialgebras
Using adjoint representation of Lie superalgebras, we obtain the matrix form
of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By
direct calculations of these identities, and use of automorphism supergroups of
two and three dimensional Lie superalgebras, we obtain and classify all two and
three dimensional Lie superbialgebras.Comment: 15 page
On factorizing -matrices in and spin chains
We consider quantum spin chains arising from -fold tensor products of the
fundamental evaluation representations of and .
Using the partial -matrix formalism from the seminal work of Maillet and
Sanchez de Santos, we derive a completely factorized expression for the
-matrix of such models and prove its equivalence to the expression obtained
by Albert, Boos, Flume and Ruhlig. A new relation between the -matrices and
the Bethe eigenvectors of these spin chains is given.Comment: 30 page
Nonlocal symmetries of integrable two-field divergent evolutionary systems
Nonlocal symmetries for exactly integrable two-field evolutionary systems of
the third order have been computed. Differentiation of the nonlocal symmetries
with respect to spatial variable gives a few nonevolutionary systems for each
evolutionary system. Zero curvature representations for some new nonevolution
systems are presented
Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
We exhibit a mapping identifying Kitaev's quantum double lattice models
explicitly as a subclass of Levin and Wen's string net models via a completion
of the local Hilbert spaces with auxiliary degrees of freedom. This
identification allows to carry over to these string net models the
representation-theoretic classification of the excitations in quantum double
models, as well as define them in arbitrary lattices, and provides an
illustration of the abstract notion of Morita equivalence. The possibility of
generalising the map to broader classes of string nets is considered.Comment: 8 pages, 6 eps figures; v2: matches published versio
Lorentz Transformations as Lie-Poisson Symmetries
We write down the Poisson structure for a relativistic particle where the
Lorentz group does not act canonically, but instead as a Poisson-Lie group. In
so doing we obtain the classical limit of a particle moving on a noncommutative
space possessing invariance. We show that if the standard mass
shell constraint is chosen for the Hamiltonian function, then the particle
interacts with the space-time. We solve for the trajectory and find that it
originates and terminates at singularities.Comment: 18 page
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