The SL(2, R) WZNW → Liouville reduction leads to a nontrivial phase space on the classical level both in 0 + 1 and 1 + 1 dimensions. To study the consequences in the quantum theory, the quantum mechanics of the 0 + 1 dimensional, point particle version of the constrained WZNW model is investigated. The spectrum and the eigenfunctions of the obtained—rather nontrivial—theory are given, and the p...

In this note we complement recent results on the exchange r-matrices appearing in the chiral WZNW model by providing a direct, purely finite-dimensional description of the relationship between the monodromy dependent 2-form that enters the chiral WZNW symplectic form and the exchange r-matrix that governs the corresponding Poisson brackets. We also develop the special case in which the exchange...

It is explained that the chiral WZNW phase space is a quasi-Poisson space with respect to the ‘canonical’ Lie quasi-bialgebra which is the classical limit of Drinfeld’s quasi-Hopf deformation of the universal enveloping algebra. This exemplifies the notion of quasi-Poisson-Lie symmetry introduced recently by Alekseev and Kosmann-Schwarzbach. PACS codes: 11.25.Hf, 11.10.Kk, 11.30.Na keywords: WZ...

It is well-known that the chiral WZNW Bloch waves satisfy a quadratic classical exchange algebra which implies the affine Kac-Moody algebra for the corresponding currents. We here obtain a direct derivation of the exchange algebra by inverting the symplectic form on the space of Bloch waves, and give a completely algorithmic construction of its generalized free field realizations that extend th...

We analyze the behavior of quarks coupled to a $SU(N_c)$ gauge theory in 1+1 dimensions. In limit strong coupling, model reduces Wess-Zumino-Novikov-Witten (WZNW) model. At nonzero density, excitations near Fermi surface form non-Fermi liquid. With $N_f$ flavors, finite density reduce free $U(1)$ field, which governs fluctuations baryon number, together with WZNW $SU(N_f)$ nonlinear sigma at le...

The equivalence between the Chern-Simons gauge theory on a threedimensional manifold with boundary and theWZNWmodel on the boundary is established in a simple and general way using the BRST symmetry. Our approach is based on restoring gauge invariance of the Chern-Simons theory in the presence of a boundary. This gives a correspondence to the WZNW model that does not require solving any constra...

This work consist of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups G with central extensions, with gauge group H being certain (infinite-dimensional) subgroup of G. We show that there exist generalized “zero-curvature” representation of the pertinent equations of motion on the ...