Euclidean quantum field theory
E9113
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
Aliases (4)
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical physics framework
→
quantum field theory → theoretical physics formalism → |
| appliesTo |
fermionic field theories
→
gauge theories → scalar field theories → |
| basedOn |
Wick rotation
→
|
| connectedTo |
classical statistical field theory
→
constructive quantum field theory → critical phenomena → functional analysis → lattice gauge theory → measure theory → probability theory → renormalization group → |
| enables |
connection to statistical mechanics
→
rigorous path integral formulation → use of functional integration techniques → |
| formalizedBy |
Osterwalder–Schrader reconstruction theorem
→
axiomatic approaches → |
| hasHistoricalDevelopment |
mid 20th century
→
|
| hasKeyConcept |
Euclidean Green’s functions
→
Euclidean action → Euclidean correlation functions → Osterwalder–Schrader axioms → Schwinger functions → analytic continuation → functional integral → lattice regularization → reflection positivity → |
| hasKeyProperty |
amenable to constructive methods
→
close analogy with classical statistical mechanics → equivalence to Minkowski theory under suitable conditions → rotational invariance in Euclidean space → |
| inspiredBy |
work of Julian Schwinger
→
work of Konrad Osterwalder → work of Kurt Symanzik → work of Robert Schrader → |
| relatedTo |
Minkowski quantum field theory
→
|
| usedIn |
finite-temperature field theory
→
lattice QCD → non-perturbative studies of quantum field theory → stochastic quantization → |
| uses |
Euclidean propagators
→
Euclidean signature metric → Gaussian measures on function spaces → Schwinger functionals → imaginary time → |
Referenced by (10)
| Subject (surface form when different) | Predicate |
|---|---|
|
Feynman path integral
("Wick rotation")
→
Feynman path integral ("Euclidean path integral") → Schwinger functions → Schwinger functions ("Wick rotation") → |
relatedTo |
|
Feynman–Kac formula
→
Schwinger functions ("statistical field theory") → |
usedIn |
|
Osterwalder–Schrader axioms
("Euclidean quantum field theories")
→
|
appliesTo |
|
Osterwalder–Schrader axioms
→
|
field |
|
Osterwalder–Schrader axioms
("Euclidean path integral")
→
|
formalism |
|
Feynman path integral
→
|
usedFor |