Wightman axioms

E284685

axiomatic system framework in mathematical physics

The Wightman axioms are a set of rigorous mathematical conditions that formalize relativistic quantum field theory in terms of operator-valued distributions on Hilbert space.

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All labels observed (6)

Label	Occurrences
Wightman axioms canonical	4
Wightman axiomatic framework	1
Wightman axioms framework	1
Wightman axioms or Osterwalder–Schrader axioms	1
Wightman formulation of quantum field theory	1
algebraic quantum field theory	1

Statements (47)

Predicate	Object
instanceOf	axiomatic system ⓘ framework in mathematical physics ⓘ
alsoKnownAs	Wightman axioms ⓘ surface form: Wightman formulation of quantum field theory Wightman framework ⓘ
appliesTo	relativistic quantum fields in Minkowski space ⓘ
assumes	Minkowski space-time ⓘ surface form: Minkowski spacetime structure
contrastsWith	canonical quantization approach ⓘ path-integral formulation of quantum field theory ⓘ
defines	n-point Wightman functions as vacuum expectation values of fields ⓘ
describes	relativistic quantum field theory ⓘ
ensures	analytic properties of correlation functions ⓘ positivity of the Hilbert space inner product ⓘ relativistic causality in quantum field theory ⓘ
field	constructive quantum field theory ⓘ mathematical physics ⓘ quantum field theory ⓘ
formalizes	relativistic quantum field theory ⓘ
goal	to provide a mathematically rigorous foundation for quantum field theory ⓘ
hasLimitation	difficulty in constructing interacting models in four dimensions ⓘ
historicalPeriod	1950s ⓘ
implies	CPT invariance under suitable assumptions ⓘ spin–statistics connection under suitable assumptions ⓘ
influenced	development of constructive quantum field theory ⓘ rigorous proofs of CPT and spin–statistics theorems ⓘ
introducedBy	Arthur Wightman ⓘ
namedAfter	Arthur Wightman ⓘ
relatedTo	Haag-Kastler axioms ⓘ surface form: Haag–Kastler axioms LSZ reduction formula ⓘ Osterwalder–Schrader axioms ⓘ algebraic quantum field theory ⓘ
requires	covariance of fields under Poincaré transformations ⓘ cyclicity of the vacuum for the field algebra ⓘ existence of a Hilbert space of states ⓘ fields as operator-valued tempered distributions ⓘ local commutativity (microcausality) ⓘ spectrum of energy–momentum in the closed forward light cone ⓘ unique Poincaré-invariant vacuum vector ⓘ unitary representation of the Poincaré group ⓘ
usesConcept	Hilbert space ⓘ Poincaré group ⓘ Wightman functions ⓘ covariance ⓘ locality ⓘ operator-valued distributions ⓘ spectrum condition ⓘ tempered distributions ⓘ vacuum state ⓘ

Referenced by (9)

Full triples — surface form annotated when it differs from this entity's canonical label.

Osterwalder–Schrader axioms → relatedTo → Wightman axioms ⓘ

Heisenberg operator formulation of quantum mechanics → influenced → Wightman axioms ⓘ

this entity surface form: algebraic quantum field theory

spin–statistics theorem → hasAlternativeFormulation → Wightman axioms ⓘ

this entity surface form: Wightman axioms framework

Yang–Mills existence and mass gap problem → involves → Wightman axioms ⓘ

this entity surface form: Wightman axioms or Osterwalder–Schrader axioms

Wightman functions → componentOf → Wightman axioms ⓘ

Haag-Ruelle scattering theory → isRelatedTo → Wightman axioms ⓘ

Wightman correlation functions → satisfies → Wightman axioms ⓘ

Wightman correlation functions → framework → Wightman axioms ⓘ

this entity surface form: Wightman axiomatic framework

Wightman axioms → alsoKnownAs → Wightman axioms ⓘ

this entity surface form: Wightman formulation of quantum field theory