A conformal net assigns von Neumann algebras of local observables to open intervals of a circle, with isotony, locality, conformal covariance, a vacuum, and positive conformal energy. Locality requires algebras for disjoint intervals to commute. It is a condition on bounded operator algebras, stronger than formal commutation of unbounded field modes. A completely rational net has the split property, strong additivity, and finite two-interval index. Strong additivity says that removing one interior point does not change the algebra generated by the two resulting interval algebras.
Conformal Net
See also
Quantum Field Theory, Vertex Operator Algebra, von Neumann AlgebraExplore with Wolfram|Alpha
References
Kawahigashi, Y. and Longo, R. "Classification of Local Conformal Nets. Case
."
Ann. Math. 160, 493-522, 2004. https://doi.org/10.4007/annals.2004.160.493.
Cite this as:
Weisstein, Eric W. "Conformal Net." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConformalNet.html