Abstract
Given a continuous representation of the Euclidean group inn+1 dimensions, together with a covariant system of subspaces, which satisfies Osterwalder-Schrader positivity, we construct a continuous unitary representation of the orthochronous Poincaré group inn+1 dimensions satisfying the spectral condition. A similar result holds for the covering groups of the Euclidean and Poincaré group.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Glimm, J. Jaffe, A. Quantum physics, New York: Springer 1981
Klein, A.: The semigroup characterization of Osterwalder-Schrader path spaces and the construction of Euclidean fields. J. Funct. Anal.27, 277–291 (1978)
Klein, A. Landau, L.: Stochastic processes associated with KMS states. J. Funct. Anal.42, 368–428 (1981)
Klein, A. Landau, L.: Construction of a unique self-adjoint generator for a symmetric local semigroup. J. Funct. Anal.44, 121–137 (1981)
Nelson, E.: Construction of quantum fields from Markoff fields. J. Funct. Anal.12, 97–112 (1973)
Osterwalder, K. Schrader, R.: Axioms for Euclidean Green's functions, I. Commun. Math. Phys.31, 83–112 (1973);II. Commun. Math. Phys.42, 281–305 (1975),
Osterwalder, K. Schrader, R.: Euclidean Fermi fields and a Feynman-Kac formula for Boson-Fermion models. Helv. Phys. Acta46, 277–302 (1973)
Atiyah, M. F., Bott, R. Shapiro, A.,: Clifford modules. Topology3, Suppl. 1, 3–38 (1964)
Dieudonné, J.: Representaciones de grupos compactos y funciones esfericas. Cursos Sem. Mat.14, Universidad de Buenos Aires 1964
Fröhlich, J.: Adv. Appl. Math.1, (1981)
Fröhlich, J., Osterwalder, K. Seiler, E.: On virtual representations of symmetric spaces and their analytic continuation (manuscript)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Partially supported by the N.S.F. under grant MCS 8202045
Rights and permissions
About this article
Cite this article
Klein, A., Landau, L.J. From the Euclidean group to the Poincaré group via Osterwalder-Schrader positivity. Commun.Math. Phys. 87, 469–484 (1983). https://doi.org/10.1007/BF01208260
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01208260