相关论文: Bicategories in field theories - an invitation

We investigate a canonical way of defining bisimilarity of systems when their semantics is given by a coreflection, typically in a category of transition systems. We use the fact, from Joyal et al., that coreflections preserve open…

The well-known calculus of fractions of Gabriel and Zisman provides a convenient way to formally invert morphisms in a category. This was generalised to bicategories by Pronk. We extend these constructions by presenting a calculus of lax…

The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…

We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these types of 2-dimensional extended topological…

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…

The first free comprehensive textbook on quantum (and classical) field theory. The approach is pragmatic, rather than traditional or artistic: It includes practical techniques, such as the 1/N expansion (color ordering) and spacecone…

I review some recent work where ideas and methods from Quantum Field Theory have proved useful in probability and vice versa. The topics discussed include the use of Renormalization Group theory in Stochastic Partial Differential Equations…

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…

There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…

Quantization of gravitational field in the neighbourhood of arbitrary nontrivial solution of Einstein equations is considered, the 2nd order of perturbation theory is calculated. The expression for quantum corrections of the field operator…

There are two ways to describe the interaction between classical and quantum information categorically: one based on completely positive maps between Frobenius algebras, the other using symmetric monoidal 2-categories. This paper makes a…

We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing…

We propose a 2-categorical formalism for describing classical information, quantum systems, and their interactions, based on the principle that classical information can be encoded as correlations between quantum systems. Applying this in…

The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…

This is an elementary review of our recent work on the classification of the spectra of those two-dimensional rational conformal field theories (RCFTs) whose (maximal) chiral algebras are current algebras. We classified all possible…

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…

We present a quantum-field-theoretic treatment of massive chiral fields in which particles possess well-defined chirality and helicity. This framework reproduces the chiral oscillation formula previously obtained in first-quantized…