The coset theory as a Hamiltonian reduction of

We show that the coset is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra  and that the corresponding W algebra is the commutant of the  quantum group.     

sl(1|2) Super-Toda Fields

Explicit exact solution of supersymmetric Toda fields associated with the Lie superalgebra sl(2|1) is constructed. The approach used is a super extension of Leznov-Saveliev algebraic analysis, which is based on a pair of chiral and antichiral Drienfeld-Sokolov systems. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie superalgebra osp(1|2). The problem lies in that a key step in the construction makes use of the tensor product decomposition of the highest weight representations of the underlying Lie superalgebra, which is not clear until recently. So our construction made in this paper presents a first explicit example of Leznov-Saveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1.     

Solvable face models related to the lie superalgebra sl(m|n)

A new series of solvable face models is presented. The Boltzmann weights are parametrized in terms of elliptic theta functions. This series generalizes the face models of type A _n ⁽¹⁾ introduced in [I].     

Universal R-matrix of the quantum superalgebra osp(2 | 1)

A quantum analogue of the simplest superalgebra osp(2 | 1) and its finite-dimensional, irreducible representations are found. The corresponding constant solution to the Yang-Baxter equation is constructed and is used to formulate the Hopf superalgebra of functions on the quantum supergroup OSp(2 | 1).     

A model of genetic code based on U_{q \to {\text{O}}} {\text{(}}sl(2) \oplus sl(2))^* {\text{)}}

The ratios of the codon usage in the quartets and sextets for 6 biological species belonging to the vertebrate series, with a statistics of codons larger than 200.000, exhibit a correlated behaviour, which fits naturally in the framework of the crystal basis model of the genetic code based on .     

Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/\hat x)\hat p + \hat p(1/\hat x) Terms

We use the dynamical invariant method to derive quantum-mechanical solution of time-dependent Hamiltonian system consisting quadratic potential, inverse quadratic potential, and . The term in Hamiltonian containing gives the expression such as in coordinate space, which we can often meet in radial equation of quantum many body problem. The wave functions differed only a time-dependent phase factor from the eigenstates of the invariant operator Î and expressed in terms of an associated Laguerre function.     

Representations of the algebra sl(2, R) and integration of Hamiltonian systems

A new representation of the sl(2, R) is given, which is related to the integrable N-particle system with inversely quadratic potential. The Hamiltonian plays the role of a raising operator and integrals correspond to highest weight vectors.     

Hamiltonian reduction of SU(2) gluodynamics

The Hamiltonian reduction of the Yang-Mills theory with the structure group SU(2) to a nonlocal model of a self-interacting 3 × 3 positive semidefinite matrix field is presented. Analysis of the field transformation properties under the action of the Poincaré group is carried out. It is shown that, in the strong coupling limit, the classical dynamics of a reduced system can be described by the local theory of interacting nonrelativistic spin-0 and spin-2 fields. A perturbation theory in powers of the inverse coupling constant g ^−2/3 that allows calculating the corrections to a leading long-wave approximation is suggested.     

En">The Second Cohomology of sl ( m | 1 ) with Coefficients in its Enveloping Algebra is Trivial

Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl ( m | 1 ) m 2, with coefficients in its enveloping algebra is trivial. The obstacles in solving the analogous problem for sl ( 3 | 2 ) are also discussed.     

Generalized Hamiltonian formalism of (2+1)-dimensional non-linear \sigma-model in polynomial formulation

We investigate the canonical structure of the (2+1)-dimensional non-linear model in a polynomial formulation. A current density defined in the non-linear model is a vector field, which satisfies a formal flatness (or pure gauge) condition. It is the polynomial formulation in which the vector field is regarded as a dynamic variable on which the flatness condition is imposed as a constraint condition by introducing a Lagrange multiplier field. The model so formulated has gauge symmetry under a transformation of the Lagrange multiplier field. We construct the generalized Hamiltonian formalism of the model explicitly by using the Dirac method for constrained systems. We derive three types of the pre-gauge-fixing Hamiltonian systems: In the first system the current algebra is realized as the fundamental Dirac Brackets. The second one manifests the similar canonical structure as the Chern-Simons or BF theories. In the last one there appears an interesting interaction as the dynamic variables are coupled to their conjugate momenta via the covariant derivative. Received: 29 September 1998 / Published online: 14 January 1999     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Graded constraint algebras,OSP(1, 1|2) and superstring theory

Earlier, we have established that, for a constrained system with a first class bosonic constraint algebra, the standard BRST invariance generalizes to an OSP(1, 1|2) symmetry, with four nilpotent and anticommuting BRST-type operators. Here we generalize this to arbitrary constrained systems with a graded first class constraint algebra. Our approach is based on the Fradkin- Vilkovisky formalism and uses a relation between abelian and nonabelian constraint algebras. Subsidiary constraints and generalized structure constants play an important role in the construction. As an application, we construct the OSP(1, 1|2) generators for superstrings. Here the subsidiary constraints are identified with physically relevant operators used in the unitarity proof.     

q-Difference Realization of Uq(sl(M|N)) and Its Application to Free Boson Realization of Uq $$(\widehat{{\text{sl}}}(2|1))$$

We present a q-difference realization of the quantum superalgebra U_q(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result, we obtain a free boson realization of the quantum affine superalgebra U_q of an arbitrary level k.     

Corrections of order O(\bar \alpha \bar \alpha _s ) and O(\overline \alpha ^2 ) to the \bar bb-decay width of the neutral Higgs boson

Analytical expressions are presented for contributions of order $O(\overline \alpha \overline \alpha _s )$ and $O(\overline \alpha ^2 )$ to the $\bar bb$ -decay width of the neutral Higgs boson of the standard model of electroweak interactions. The numerical value of the mixed QED and QCD correction of order $O(\overline \alpha \overline \alpha _s )$ is comparable to other computed terms in the perturbation series.     

Eleven-dimensional gauge theory for the M-algebra as an Abelian semigroup expansion of \mathfrak{osp} ( 32 | 1 )

A new Lagrangian realizing the symmetry of the M-algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian semigroup expansion, a link between the M-algebra and the orthosymplectic algebra is established, and an M-algebra-invariant symmetric tensor of rank six is computed. This symmetric invariant tensor is a key ingredient in the construction of the new Lagrangian. The gauge-invariant Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a subspace separation method based on the extended Cartan homotopy formula.     

Kosterlitz-Thouless transition for the finite-temperatured=2+1,U(1) Hamiltonian lattice gauge theory

We prove that in thed=2+1,U(1) Hamiltonian (continuous time) lattice gauge theory the confining potential between two static external charges grows logarithmically with their distance, at sufficiently high temperatures. As it is known that for zero or low temperatures and large coupling constant the model confines linearly, we have therefore established the existence of a Kosterlitz-Thouless transition. Our results are based on a Mermin-Wagner type of argument combined with correlation inequalities and known results for the two-dimensional (spin) Villain model.     

Representations of \mathcal{U}_q (sl(3)) at roots of 1 (In the restricted specialisation)

Irreducible representations of at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra not to be completely diagonalised. Some irreducible representations of indeed contain indecomposable -modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation.