Abstract
Given a half-sided modular standard inclusion (N ⊂ ℳ, Ω) of von-Neumann algebras which is conormal, we construct a chiral conformal quantum field theory on the circle. Conversely, a conformal quantum field theory on the circle which fulfills, in addition, the property of strong additivity, yields such data in a natural way.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bisognano, J. and Wichmann, E., On the duality condition for a Hermitean scalar field,J. Math. Phys. 16, 985 (1975).
Borchers, H.-J., The CPT-Theorem in two-dimensional theories of local observables,Comm. Math. Phys. 143, 315 (1992).
Buchholz, D., Mack, G. and Todorov, I., The current algebra on the circle as a germ of local field theories,Nuclear Phys. B, Proc. Suppl. 56, 20 (1988).
Buchholz, D. and Schulz-Mirbach, H., Haag duality in conformal quantum field theory,Rev. Math. Phys. 2, 105, (1990).
Doplicher, S. and Longo R., Standard and split inclusions of von-Neumann-algebras,Invent. Math. 75, 493 (1984).
Guido, D. and Longo, R., Relativistic invariance and charge conjugation in quantum field theory,Comm. Math. Phys. 148, 521 (1992).
Longo, R., Solution of the factorial Stone-Weierstrass Conjecture,Invent. Math. 76, 145 (1984).
Haag, R.,Local Quantum Physics, Springer-Verlag, New York, 1992.
Wassermann, A., Subfactors arising from positive energy representations of some infinite dimensional groups, preliminary notes.
Wiesbrock, H.-W., Half-sided modular inclusions of von Neumann-algebras,Comm. Math. Phys. 157, 83 (1993).
Wiesbrock, H.-W., Conformal quantum field theory and half-sided modular inclusions of von Neumann algebras,Comm. Math. Phys. 158, 537 (1993).
Author information
Authors and Affiliations
Additional information
Partly supported by the DFG, SFB 288 ‘Differentialgeometrie und Quantenphysik’.
Rights and permissions
About this article
Cite this article
Wiesbrock, HW. A note on strongly additive conformal field theory and half-sided modular conormal standard inclusions. Lett Math Phys 31, 303–307 (1994). https://doi.org/10.1007/BF00762793
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00762793