# Category: Axiomatic quantum field theory

Axiomatic quantum field theory
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator alg
Wightman axioms
In mathematical physics, the Wightman axioms (also called Gårding–Wightman axioms), named after Arthur Wightman, are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur
Schwinger function
In quantum field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to the ordered set of points in Euclidean space wi
CCR and CAR algebras
In mathematics and physics CCR algebras (after canonical commutation relations) and CAR algebras (after canonical anticommutation relations) arise from the quantum mechanical study of bosons and fermi
Logarithmic Sobolev inequalities
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leona
Edge-of-the-wedge theorem
In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the
Cluster decomposition
In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum exp
Operator product expansion
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to q
Haag's theorem
While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now common
Constructive quantum field theory
In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise mathematical structures. This demonstration requ
Local quantum field theory
The Haag–Kastler axiomatic framework for quantum field theory, introduced by Haag and Kastler, is an application to local quantum physics of C*-algebra theory. Because of this it is also known as alge
Algebraic holography
Algebraic holography, also sometimes called Rehren duality, is an attempt to understand the holographic principle of quantum gravity within the framework of algebraic quantum field theory, due to Karl
Reeh–Schlieder theorem
The Reeh–Schlieder theorem is a result in relativistic local quantum field theory published by and (1918-2003) in 1961. The theorem states that the vacuum state is a cyclic vector for the field algebr
Borchers algebra
In mathematics, a Borchers algebra or Borchers–Uhlmann algebra or BU-algebra is the tensor algebra of a vector space, often a space of smooth test functions. They were studied by H. J. Borchers, who s
Gelfand–Naimark–Segal construction
In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain lin
Bogoliubov causality condition
Bogoliubov causality condition is a causality condition for scattering matrix (S-matrix) in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bo