Coleman theorem on symmetry breaking in two dimensions
E573375
The Coleman theorem on symmetry breaking in two dimensions is a result in quantum field theory stating that continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime due to large infrared fluctuations.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Mermin–Wagner theorem | 1 |
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
no-go theorem
ⓘ
theorem in quantum field theory ⓘ |
| appliesTo |
1+1 dimensional relativistic quantum field theories
ⓘ
two-dimensional spacetime ⓘ |
| assumes |
existence of a unique translationally invariant vacuum
ⓘ
locality ⓘ positivity of the Hilbert space metric ⓘ relativistic invariance ⓘ short-range interactions ⓘ |
| clarifies | conditions under which Goldstone’s theorem fails in two dimensions ⓘ |
| concerns |
continuous global symmetries
ⓘ
spontaneous symmetry breaking ⓘ |
| consequence |
no phase with spontaneously broken continuous symmetry exists in 1+1D relativistic QFT under its assumptions
ⓘ
order parameters for continuous symmetries cannot acquire nonzero vacuum expectation values in 1+1D ⓘ |
| doesNotApplyTo |
discrete symmetries
ⓘ
higher-dimensional spacetimes ⓘ |
| excludes | long-range order associated with continuous symmetries in two-dimensional relativistic QFT ⓘ |
| field |
quantum field theory
ⓘ
theoretical physics ⓘ |
| formalism | operator formalism of quantum field theory ⓘ |
| holdsFor |
continuous internal symmetries
ⓘ
global symmetries ⓘ |
| implies |
absence of Goldstone bosons for continuous symmetries in two-dimensional relativistic quantum field theories
ⓘ
vacuum expectation values of local order parameters for continuous symmetries vanish in two dimensions ⓘ |
| influenced | understanding of phase structure in low-dimensional quantum field theories ⓘ |
| involves |
cluster decomposition properties
ⓘ
correlation functions of fields ⓘ infrared behavior of propagators ⓘ |
| mathematicalContext | relativistic quantum fields on two-dimensional Minkowski space ⓘ |
| namedAfter | Sidney Coleman NERFINISHED ⓘ |
| originalAuthor | Sidney Coleman NERFINISHED ⓘ |
| publishedIn | Communications in Mathematical Physics NERFINISHED ⓘ |
| reason | large infrared fluctuations of massless modes in two dimensions ⓘ |
| relatedTo |
Goldstone theorem
NERFINISHED
ⓘ
Mermin–Wagner theorem NERFINISHED ⓘ infrared divergences ⓘ massless scalar fields in two dimensions ⓘ |
| statesThat | continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime ⓘ |
| typeOf | infrared no-go result ⓘ |
| usedIn |
analysis of two-dimensional sigma models
ⓘ
constraining model building in 1+1 dimensional QFT ⓘ study of two-dimensional scalar field theories ⓘ |
| yearProposed | 1973 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Mermin–Wagner theorem