Concepts in Hadron Physics : Proceedings of the X. Internationale Universitatswochen fur Kernphysik 1971 der Karl-Franzens-Universitat Graz, at Schladming (Steiermark, Austria), 1st March - 13th March PDF
Edited by Paul Urban
Part of the Few-Body Systems series
Description
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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Download - Immediately Available
- Format:PDF
- Publisher:Springer Vienna
- Publication Date:06/12/2012
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- ISBN:9783709182840
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Vienna
- Publication Date:06/12/2012
- Category:
- ISBN:9783709182840
