Related papers: Higher Structures in Algebraic Quantum Field Theor…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
In this paper we present a new algebraic structure (a super hyperbolic system in our terminology) for finite quantum systems, which is a generalization of the usual one in the two-level system. It fits into the so-called generalized Pauli…
In this paper we will analyse some interesting structures that occur in scalar quantum field theory. We will quantize this theory using path integrals. We will analyse the Bogomolny Bound for scalar quantum field theory in two dimensions.…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
There is a fruitful interplay between algebraic geometry on the one side and perturbative quantum field theory on the other side. I review the main relevant mathematical concepts of periods, Hodge structures and Picard-Fuchs equations and…
In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).
In this article, we review some of the recent developments towards the future goal of quantum computing or quantum simulating lattice QCD. This includes a novel theoretical framework developed for non-Abelian gauge theories that is the…
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…
A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
Costello and Gwilliam have given both 1) a general definition of perturbative quantum gauge theory on a manifold M and 2) a construction of a factorization algebra of quantum observables assigned to every quantum gauge theory. In this…