Osterwalder–Schrader axioms
E59638
The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
Observed surface forms (2)
| Surface form | Occurrences |
|---|---|
| Osterwalder–Schrader reconstruction theorem | 2 |
| Wightman axioms for the reconstructed Minkowski theory | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
axiomatic system
ⓘ
set of mathematical conditions ⓘ |
| allows | reconstruction of relativistic quantum field theories from Euclidean correlation functions ⓘ |
| appliesTo |
Euclidean quantum field theory
ⓘ
surface form:
Euclidean quantum field theories
|
| assumes |
Euclidean space
ⓘ
surface form:
Euclidean space-time
|
| basedOn |
Euclidean invariance
ⓘ
cluster properties ⓘ reflection positivity ⓘ regularity conditions ⓘ symmetry ⓘ |
| characterizes | which Euclidean field theories correspond to physical relativistic theories ⓘ |
| concerns |
Euclidean correlation functions
ⓘ
Schwinger functions ⓘ |
| context |
probability measures on spaces of distributions
ⓘ
rigorous quantum field theory ⓘ |
| field |
Euclidean quantum field theory
ⓘ
mathematical physics ⓘ quantum field theory ⓘ |
| formalism |
Euclidean quantum field theory
ⓘ
surface form:
Euclidean path integral
|
| guarantees |
locality of the reconstructed quantum fields
ⓘ
positivity of the inner product after reconstruction ⓘ spectrum condition for the Hamiltonian ⓘ |
| implies |
Osterwalder–Schrader axioms
self-linksurface differs
ⓘ
surface form:
Wightman axioms for the reconstructed Minkowski theory
existence of a Hilbert space of states ⓘ existence of a self-adjoint Hamiltonian ⓘ unitary representation of the Poincaré group after continuation ⓘ |
| includesCondition |
Euclidean invariance of Schwinger functions
ⓘ
cluster decomposition property ⓘ reflection positivity of Schwinger functions ⓘ regularity and growth bounds on Schwinger functions ⓘ symmetry of Schwinger functions under permutations of arguments ⓘ |
| introducedBy |
Konrad Osterwalder
ⓘ
Robert Schrader ⓘ |
| namedAfter |
Konrad Osterwalder
ⓘ
Robert Schrader NERFINISHED ⓘ |
| publicationType | results published in mathematical physics papers ⓘ |
| purpose |
to allow analytic continuation from Euclidean to Minkowski space
ⓘ
to characterize Euclidean quantum field theories that correspond to relativistic quantum field theories ⓘ |
| relatedTo |
Minkowski space quantum field theory
ⓘ
Schwinger functions ⓘ Wightman axioms ⓘ analytic continuation ⓘ |
| requires | reflection with respect to a Euclidean time coordinate ⓘ |
| timePeriod | 1970s ⓘ |
| usedFor |
constructive quantum field theory
ⓘ
rigorous formulation of quantum field theory ⓘ |
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Osterwalder–Schrader reconstruction theorem
this entity surface form:
Wightman axioms for the reconstructed Minkowski theory
this entity surface form:
Osterwalder–Schrader reconstruction theorem