Related papers: Free Variable Loop Equations for the 3-State Potts…
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on self-dual strip graphs $G$ of the square lattice with fixed width $L_y$ and arbitrarily great length $L_x$…
The field equations for both generic bosonic and generic locally supersymmetric 2D dilatonic gravity theories in the absence of matter are written as free differential algebras. This constitutes a generalization of the gauge theoretic…
We derive the Schwinger-Dyson/loop equations for the USp(2k) matrix model which close among the closed and open Wilson loop variables. These loop equations exhibit a complete set of the joining and splitting interactions required for the…
In the example of $R^2+T^2$ gravity on the unit two dimensional disk we demonstrate that in the presence of an independent spin connection it is possible to define local gauge invariant boundary conditions even on boundaries which are not…
We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential…
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the…
In this paper, an attempt is made to represent 5+1 dimensional gravity (via ADM formalism) in terms of the loop constructions introduced by the author in a companion paper. The "momenta" and "velocity" from the earlier paper, which were…
In the first part of the talk, I review the applications of loop equations to the matrix models and to 2-dimensional quantum gravity which is defined as their continuum limit. The results concerning multi-loop correlators for low genera and…
We study disk amplitudes whose boundaries have heterogeneous matter states in a system of $(4,5)$ conformal matter coupled to 2-dim gravity. They are analysed by using the 3-matrix chain model in the large $N$ limit. Each of the boundaries…
A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross-sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is…
Following Toomre & Kalnajs (1991), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation…
We formulate a natural model of current loops and magnetic monopoles for arbitrary planar graphs, which we call the monopole-dimer model, and express the partition function of this model as a determinant. We then extend the method of…
We exploit the identification between the critical theory of the 3-state Potts model and the D_5 conformal model. This allows us to determine all 3-point correlations involving the fields associated with the Potts order parameter and the…
The concept of freely falling frames suggests that gravity exhibits a local Lorentz gauge symmetry and requires a background Minkowski reference frame. The gauge vector fields of a Yang-Mills-type theory can be constructed from the…
We write down the Yang-Mills partition function and the average Wilson loop in terms of local gauge-invariant variables being the six components of the metric tensor of dual space. The Wilson loop becomes the trace of the parallel…
We compute the distance-dependent three-point function of general planar maps and of bipartite planar maps, i.e., the generating function of these maps with three marked vertices at prescribed pairwise distances. Explicit expressions are…
We build a new technique to generate rotation from arbitrary static solutions that asymptote to four- or five-dimensional Minkowski spacetime. The method is purely algebraic and does not require solving Einstein equations. It proceeds by…
For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a…