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Soluble quantum field theory models are a rare commodity. An infinite number of degrees of freedom and noncompact invariance groups have a nasty habit of ex ploding in the model-makers' face. Nevertheless, impor tant progress has recently been made in the class of superrenormalizable relativistic theories, such as a self-interacting boson in a two-dimensional space time [ 1]. These results have been obtained starting with the free field and adding the interaction in a carefully controlled way. Yet, the models successfully studied in this way do DQ~ have an infinite field strength renormalization, which, at least according to perturbation theory, should appear for realistic relativistic models in four-dimensional space time. ~2~!Y~~!9n_~g_~h~_~gg~1 The ultralocal scalar field theories discussed in these lecture notes are likewise motivated by relativistic theories but are based on a different approximatiGn. This approximation formally amounts to dropping the spatial gradient term from the Hamiltonian rather than the non linear interaction. For a self-interacting boson field in a space-time of (s+l) dimensions (s~l), the classical ultralocal model Hamiltonian reads (1-1) The quantum theory of this model is the subject of the present paper. This model differs formally from a rela tivistic theory by the term f![Z~Cl(~)]2 d~ which, it is hoped, can, in one or another way, be added as a pertur 229 bation in the quantum theory. However, that still remains a problem for the future, and we confine our remarks to . . a careful study of the "unperturbed" model (1-1).
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Table of contents (18 papers)
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Front Matter
Editors and Affiliations
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Bibliographic Information
Book Title: Concepts in Hadron Physics
Book Subtitle: Proceedings of the X. Internationale Universitätswochen für Kernphysik 1971 der Karl-Franzens-Universität Graz, at Schladming (Steiermark, Austria), 1st March – 13th March 1971
Editors: Paul Urban
Series Title: Few-Body Systems
DOI: https://doi.org/10.1007/978-3-7091-8284-0
Publisher: Springer Vienna
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag / Wien 1971
Softcover ISBN: 978-3-7091-8286-4Published: 25 January 2012
eBook ISBN: 978-3-7091-8284-0Published: 06 December 2012
Edition Number: 1
Number of Pages: XVII, 424
Topics: Elementary Particles, Quantum Field Theory, Engineering Economics, Organization, Logistics, Marketing