M. Mintchev

Perturbative aspects of the Chern-Simons field theory

Abstract The quantization of the non-abelian Chern-Simons theory in three dimensions is performed in the framework of the BRS formalism. General covariance is preserved on the physical subspace. The perturbative analysis at two loops confirms that the model is finite. To this order, the radiative corrections to the two- and three-point proper vertices vanish.

Chern-Simons holonomies and the appearance of quantum groups

Abstract The monodromy representation defined by the quantum holonomies and realized on the physical state space of the Chern-Simons model is investigated. It is shown that this representation naturally extends to a representation of the braid group related to a particular solution of the quantum Yang-Baxter equation. The presence of a hidden quantum group symmetry is established.

Braids and Quantum Group Symmetry in {Chern-Simons} Theory

Abstract The monodromy matrices defined by the quantum holonomies acting on the physical state space of the Chern-Simons theory are derived. Up to equivalence, these matrices are reconstructed by means of a matrix-valued gauge connection satisfying the Gauss law. In terms of this connection, the relation of the Chern-Simons model with conformal field theory and quantum group is established. The braid group representation realized on the physical states is obtained. The quantum group symmetry appears as a hidden symmetry of the quantized theory.

Scattering in the presence of a reflecting and transmitting impurity

We investigate factorized scattering from a reflecting and transmitting impurity. Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not only on their difference. We show that a specific extension of a boundary algebra encodes the underlying scattering theory. The total scattering operator is constructed in this framework and shown to be unitary.

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a finite number of particles N, the Renyi entanglement entropies grow as log N, with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite-size scaling forms of the corrections to the scaling.

Reflection–transmission algebras

Inspired by factorized scattering from δ-type impurities in (1 + 1)-dimensional spacetime, 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 are explicitly constructed and a general factorized scattering theory is developed in this framework.

Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line

We describe an algebraic framework for studying the symmetry properties of integrable quantum systems on the half line. The approach is based on the introduction of boundary operators. It turns out that these operators both encode the boundary conditions and generate integrals of motion. We use this direct relationship between boundary conditions and symmetry content to establish the spontaneous breakdown of some internal symmetries, due to the boundary.

Chern-Simons model and new relations between the HOMFLY coefficients

Abstract Using the connection between the vacuum expectation value of the Wilson line operator W T (C) in the Chern-Simons field theory and the HOMFLY polynomial associated with the knot C, we derive new relations between the HOMFLY coefficients. An explicit analytic expression for the second coefficient of the Alexander-Conway polynomial is presented.

Fock representations of quantum fields with generalized statistics

We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics. The main features of these representations are investigated. Various aspects of the underlying mathematical structure are illustrated by means of explicit examples.

The quantum nonlinear Schrödinger model with point-like defect

We establish a family of point-like impurities which preserve the quantum integrability of the nonlinear Schrodinger model in 1+1 spacetime dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection–transmission algebra. The basic physical properties of the solution, including the spacetime symmetry of the bulk scattering matrix, are also discussed.