We study the effective actions S (k) obtained by k iterations of a renormalization transformation of the U(1) Higgs model in d=2 or 3 space-time dimensions. We identify a quadratic approximation S (k) Q to S (k) which we call mean field theory, and which will serve as the starting point for a convergent expansion of the Green’s functions, uniformly in the lattice spacing. Here we show how the approximations S (k) Q arise and how to handle gauge fixing, necessary for the analysis of the continuum limit. We also establish stability bounds on S (k) Q uniformly in k. This is an essential step toward proving the existence of a gap in the mass spectrum and exponential decay of gauge invariant correlations.
Supported in part by the National Science Foundation under Grant PHY 82-03669
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Similar content being viewed by others ReferencesBafaban, T., Imbrie, J., Jaffe, A.: Exact renormalization group for gauge theories, 1983 Cargese Lectures, Progress in Gauge Field Theories, pp. 79–104. G. ’tHoof et al. (ed.). New York: Plenum Press 1984
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Tadeusz Balaban
Present address: Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA
Lyman Laboratory of Physics, Harvard University, Cambridge, MA, 02138, USA
Tadeusz Balaban, John Imbrie & Arthur Jaffe
Department of Physics, Lyman Laboratory of Physics, Harvard University, Cambridge, MA, 02138, USA
Arthur Jaffe
II. Institut für Theoretische Physik der Universität Hamburg, D-2000, Hamburg 50, Fed. Rep. of Germany
Harry Lehmann & Gerhard Mack &
© 1985 Springer-Verlag Berlin, Heidelberg
About this chapter Cite this chapterBalaban, T., Imbrie, J., Jaffe, A. (1985). Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory. In: Jaffe, A., Lehmann, H., Mack, G. (eds) Quantum Field Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70307-2_17
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15260-6
Online ISBN: 978-3-642-70307-2
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