Related papers: Fermionic reflection matrices
The graded reflection equation is investigated for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model. We have found four classes of diagonal solutions and twelve classes of non-diagonal ones. The number of free parameters for some solutions depends…
The graded reflection equation is investigated for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model. We have found four classes of diagonal solutions with at the most one free parameter and twelve classes of non-diagonal ones with the number of…
We propose a classification of the solutions of the graded reflection equations to the $U_{q}[spo(2n|2m)]$ vertex model. We find twelve distinct classes of reflection matrices such that four of them are diagonal. In the non-diagonal…
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in…
We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted…
The realistic free fermionic models have had remarkable success in providing plausible explanations for various properties of the Standard Model which include the natural appearance of three generations, the explanation of the heavy top…
We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a…
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra…
Bosonic formulas for generating series of partitions with certain restrictions are obtained by solving a set of linear matrix q-difference equations. Some particular cases are related to combinatorial problems arising from solvable lattice…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
We explore different limits of exactly solvable vector and matrix fermionic quantum mechanical models with quartic interactions at finite temperature. The models preserve a $U(1)\times SU(N)\times SU(L)$ symmetry at the classical level and…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…
Representability conditions on the one- and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals. A positivity condition for a certain kind of Grassmann integral is established which, in turn,…
We develop a first and second fundamental theorem for $n$--tuples of bosonic and fermionic matrices, by developing graded analogues of the classical case.
Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in…