Related papers: Constructive Tensor Field Theory
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by…
We discuss the problem to develop a mathematical theory of a certain class of nonrational conformal field theories (CFT) which contain the unitary CFT. A variant of the concept of a modular functor is proposed that appears to be suitable…
Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…
The Landau-Ginzburg/Conformal Field Theory correspondence predicts tensor equivalences between categories of matrix factorisations of certain polynomials and categories associated to the $N=2$ supersymmetric conformal field theories. We…
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…
We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field…
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…
I wrote this book in a "do-it-yourself" style so that I give only a draft of tensor theory, which includes formulating definitions and theorems and giving basic ideas and formulas. All other work such as proving consistence of definitions,…
The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is…
This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.
Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, $d$ and $*$ which are used to describe…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
In this paper we give an algorithmic description of Freyd categories that subsumes and enhances the usual approach to finitely presented modules in computer algebra. The upshot is a constructive approach to finitely presented functors that…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
It is conceivable that the construction of the energy--momentum tensor (EMT) in lattice field theory enlarges our ability in lattice field theory and also deepens our understanding on EMT at the non-pertubative level. In this talk, I will…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…