Related papers: The $\tau_2$ model and parafermions
We introduce a Frobenius-like structure for the $\frak{sl}_2$ Gaudin model. Namely, we introduce potential functions of the first and second kind. We describe the Shapovalov form in terms of derivatives of the potential of the first kind…
Symmetries and solutions of the Painleve IV equation are presented in an alternative framework which provides the bridge between the Hamiltonian formalism and the symmetric Painleve IV equation. This approach originates from a method…
We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
We consider the semiclassical approximation to the spectral form factor K(tau) for two-dimensional uniformly hyperbolic systems, and derive the first off-diagonal correction for small tau. The result agrees with the tau^2-term of the form…
The question about asymptotical behaviour of solutions for the system $\dot x=A_\nu x+f$ for big values of the parameter $\nu\in\frak A$ is considered. An approach to the reduction of a large class of problems to easily solvable problem…
Lie-Poisson gauge formalism provides a semiclassical description of noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson…
We show how to bosonize two-dimensional non-abelian models using finite chiral determinants calculated from a Gauss decomposition. The calculation is quite straightforward and hardly more involved than for the abelian case. In particular,…
We present an extension of the deformation method applied to self-dual solutions of generalized Abelian Higgs-Chern-Simons models. Starting from a model defined by a potential $V(| \phi |)$ and a non-canonical kinetic term $\omega(| \phi |)…
We investigate a class of conformal Non-Abelian-Toda models representing a noncompact $SL(2,R)/U(1)$ parafermionions (PF) interacting with a specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the…
We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with H\"older continuous coefficients. The result we obtain is essentially based on parametrix method.
We introduce the notion of parafermionic fields as the chiral fields which describe particle excitations in two-dimensional conformal field theory, and argue that the parafermionic conformal dimensions can be determined using scale…
Nodal solutions of a parametric (p_1,p_2)-Laplacian system, with Neumann boundary conditions, are obtained by chiefly constructing appropriate sub-super-solution pairs.
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…
Analyzing an $SU_L(2)$-chiral gauge theory with external multifermion couplings, we find a possible scaling region where doublers decouple by acquiring chiral-invariant masses and $\psi_R$ is free mode owing to the $\psi_R$-shift-symmetry,…
A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…
We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…
We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor…
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…