Abstract
A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Araki H., Haag R.: Collision cross sections in terms of local observables. Commun. Math. Phys. 4, 77–91 (1967)
Arveson, W.: The harmonic analysis of automorphism groups. In: Operator algebras and applications. I. Proceedings of Symposia in Pure Mathematics, vol. 38, pp. 255–307. American Mathematical Society, Providence (1982)
Bostelmann, H.: Lokale Algebren und Operatorprodukte am Punkt, Ph.D. Thesis. Universitäat Göttingen (2000). http://webdoc.sub.gwdg.de/diss/2000/bostelmann/
Bostelmann H.: Phase space properties and the short distance structure in quantum field theory. J. Math. Phys. 46, 052301–052318 (2005)
Bostelmann H.: Operator product expansions as a consequence of phase space properties. J. Math. Phys. 46, 082304–082317 (2005)
Buchholz D.: Harmonic analysis of local operators. Commun. Math. Phys. 129, 631–641 (1990)
Buchholz D.: Phase space properties of local observables and structure of scaling limits. Ann. Inst. H. Poincaré 64, 433–459 (1996)
Buchholz D., D’Antoni C., Longo R.: The universal structure of local algebras. Commun. Math. Phys. 111, 123–135 (1987)
Buchholz D., Jacobi P.: On the nuclearity condition for massless fields. Lett. Math. Phys. 13, 313–323 (1987)
Buchholz D., Junglas P.: On the existence of equilibrium states in local quantum field theory. Commun. Math. Phys. 121, 255–270 (1989)
Buchholz D., Porrmann M.: How small is the phase space in quantum field theory?. Ann. Inst. H. Poincaré 52, 237–257 (1990)
Buchholz D., Summers S.J.: Scattering in relativistic quantum field theory: fundamental concepts and tools. In: Francoise, J.-P., Naber, G., Tsun, T.S.(eds) Encyclopedia of Mathematical Physics, vol. 4, pp. 456–465. Elsevier, New York (2006) Preprint math-ph/0509047
Buchholz D., Wanzenberg R.: The realm of the vacuum. Commun. Math. Phys. 143, 577–589 (1992)
Buchholz D., Wichmann E.H.: Causal independence and the energy-level density of states in local quantum field theory. Commun. Math. Phys. 106, 321–344 (1986)
Dybalski, W.: A sharpened nuclearity condition and the uniqueness of the vacuum in QFT. Commun. Math. Phys. Preprint arXiv:0706.4049v2 (to appear)
Haag R.: Local Quantum Physics. Springer, Berlin (1992)
Haag R., Swieca J.A.: When does a quantum field theory describe particles?. Commun. Math. Phys. 1, 308–320 (1965)
Kosaki H.: On the continuity of the map \({\phi\to |\phi|}\) from the predual of a W *-algebra. J. Funct. Anal. 59, 123–131 (1984)
Lechner G.: Construction of quantum field theories with factorizing S-matrices. Commun. Math. Phys. 277, 821–860 (2008)
Porrmann M.: Particle Weights and their Disintegration I. Commun. Math. Phys. 248, 269–304 (2004)
Porrmann M.: Particle weights and their disintegration II. Commun. Math. Phys. 248, 305–333 (2004)
Reed M., Simon B.: Methods of Modern Mathematical Physics. Part II: Fourier Analysis, Self-Adjointness. Academic Press, New York (1975)
Acknowledgements
I would like to thank Prof. D. Buchholz for his continuing advice and encouragement in the course of this work. Financial support from Deutsche Forschungsgemeinschaft is gratefully acknowledged.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Dybalski, W. A Sharpened Nuclearity Condition for Massless Fields. Lett Math Phys 84, 217–230 (2008). https://doi.org/10.1007/s11005-008-0244-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-008-0244-9