Related papers: Free Variables and the Two Matrix Model
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
The Euclidian thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space is written as the real part of a complex analytic function of a variable that conformally maps the infinite strip…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particular, we show that if the nonlinear term possesses a special…
We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an…
We describe a structure of PRO on hypermatrices. This structure allows us to define multilinear representations of PROs and in particular of free Pros. As an example of applications, we investigate the relations of the representations of…
Relativistic formalism of Green's functions is dicussed in QCD and QED,where the relativistic Green's functions are constructed using the Schwinger proper time formalism and the Fock-Feynman-Schwinger method.As a result a simple and exact…
We elaborate on the method of differential equations for evaluating Feynman integrals. We focus on systems of equations for master integrals having a linear dependence on the dimensional parameter. For these systems we identify the criteria…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain with…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation…
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the…
In this article, we present the general form of the full electromagnetic Green function which is suitable for the application in bulk materials physics. In particular, we show how the seven adjustable parameter functions of the free Green…
The free energy of the Penner model is shown to be closely related to the integral over the two diagonalizing unitary matrices of a complex rectangular matrix.
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the…
We revisit the long standing problem of the geometric free variable approach to computing the generating function for disk amplitudes in the matrix model formulation of the 3-state Potts model coupled to 2D discrete gravity. This method is…
We calculate the Green functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both noncommutative products, for which there…