Related papers: An Introduction To The Web-Based Formalism
Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius…
The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…
A low energy string theory should reduce to an ordinary quantum field theory, but in reality the structures of the two are so different as to make the equivalence obscure. The string formalism is more symmetrical between the spacetime and…
We describe a non-extensional variant of Martin-L\"of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…
I report on work on a Lagrangian formulation for the simplest 1+1 dimensional integrable hierarchies. This formulation makes the relationship between conformal field theories and (quantized) 1+1 dimensional integrable hierarchies very…
A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…
This paper is based on the author's paper "Koszul duality in deformation quantization, I", with some improvements. In particular, an Introduction is added, and the convergence of the spectral sequence in Lemma 2.1 is rigorously proven. Some…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…
We summarize common notations and concepts in the field of Intrinsic Alignments (IA). IA refers to physical correlations involving galaxy shapes, galaxy spins, and the underlying cosmic web. Its characterization is an important aspect of…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
This article is a concise review of covariant string field theory prepared for the Encyclopedia of Mathematical Physics, Elsevier (2006). Referencing follows the publisher's guidelines.
This article is the first in a series of articles that explain the formalization of a constructive model of cubical type theory in Nuprl. In this document we discuss only the parts of the formalization that do not depend on the choice of…
Given two conformal field theories related to each other by a marginal perturbation, and string field theories constructed around such backgrounds, we show how to construct explicit redefinition of string fields which relate these two…
This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec.…