相关论文: Taking N to zero with S matrices
We explain how to use computer experiments over finite fields to gain heuristic information about the solution set of polynomial equations in characteristic zero. These are notes of a tutorial I gave at the NATO Advanced Study Institute on…
This is a contribution to the number theory of the dimer problem. The number of dimer coverings (i.e., perfect matchings) of a square lattice graph is discussed modulo powers of 2.
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with…
We study skew polycyclic codes over a finite field $\mathbb{F}_q$, associated with a skew polynomial $f(x) \in \mathbb{F}_q[x;\sigma]$, where $\sigma$ is an automorphism of $\mathbb{F}_q$. We start by proving the Roos-like bound for both…
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are…
We define an $S$-matrix for massive scalar fields on a fixed de Sitter spacetime, in the expanding patch co-ordinates relevant for early Universe cosmology. It enjoys many of the same properties as its Minkowski counterpart, for instance:…
We propose a field-theoretical approach to a polymer system immersed in an ideal mixture of clustering centers. The system contains several species of these clustering centers with different functionality, each of which connects a fixed…
The parquet approximation in the matrix Higgs model is considered. We demonstrate analytically that in the large $N$ limit the parquet approximation gives an satisfying agreement with the exact results. It is shown that the parquet planar…
Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary…
We give an indication that gravity coupled to an infinite number of fields might be a renormalizable theory. A toy model with an infinite number of interacting fermions in four-dimentional space-time is analyzed. The model is finite at any…
This talk is based on a recent paper$^{1}$ of ours. In an attempt to understand three-dimensional conformal field theories, we study in detail one such example --the large $N$ limit of the $O(N)$ non-linear sigma model at its non-trivial…
We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists…
A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…
This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field…
A parquet approximation (generalized ladder diagrams) in matrix models is considered. By means of numerical calculations we demonstrate that in the large $N$ limit the parquet approximation gives an excellent agreement with exact results.
Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…