Related papers: Heisenberg-picture quantum field theory
In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…
In this short letter we review Schwinger's formulation of Quantum Mechanics and we argue that the mathematical structure behind Schwinger's "Symbolism of Atomic Measurements" is that of a groupoid. In this framework, both the Hilbert space…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a…
In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories that vertex algebras have to one…
This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor category of a monoidal category. The key…
It is generally assumed that quantum field theory (QFT) is gauge invariant. However it is well known that non-gauge invariant terms appear in various calculations. This problem was recently examined in [9] for a "simple" field theory and it…
Following P. A. M. Dirac's critique in ``Lectures on Quantum Field Theory'' of the usual formalism, I will discuss the role of the time parameter to solve R. Haag's no-go theorem on the non-equivalence of the conventional Schr\"odinger…
Given an algebraic theory which can be described by a (possibly symmetric) operad $P$, we propose a definition of the \emph{weakening} (or \emph{categorification}) of the theory, in which equations that hold strictly for $P$-algebras hold…
A quantum field theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and…
Dynamics of a class of quantum field models on 1d lattice in Heisenberg picture is mapped into a class of `quantum chaotic' one-body systems on configurational 2d torus (or 2d lattice) in Schr\" odinger picture. Continuum field limit of the…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represent statistics using super vector spaces. Unitarity is…
Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive…
For $G$ a finite group, we prove in dimension 2 that there is a monoidal equivalence between the category of $G$-equivariant topological quantum field theories and the category of $G$-Frobenius algebras, this was proved by G. Moore and G.…
This paper charts a very direct path between the categorical approach to quantum mechanics, due to Abramsky and Coecke, and the older convex-operational approach based on ordered vector spaces (recently reincarnated as "generalized…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 1 - The classical Heisenberg model: Non-Abelian symmetries; The generators of the…