Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory
Dec, 198464 pages
Published in:
- Commun.Math.Phys. 97 (1985) 299
DOI:
Report number:
- HUTMP-84/B171
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Abstract: (Springer)
We study the effective actionsS(k) obtained byk iterations of a renormalization transformation of the U(1) Higgs model ind=2 or 3 spacetime dimensions. We identify a quadratic approximationSQ(k) toS(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 approximationsSQ(k) arise and how to handle gauge fixing, necessary for the analysis of the continuum limit. We also establish stability bounds onSQ(k), uniformly ink. This is an essential step toward proving the existence of a gap in the mass spectrum and exponential decay of gauge invariant correlations.Note:
- Dedicated to memory of K. Symanzik
- MODEL: HIGGS
- GAUGE FIELD THEORY: U(1)
- LATTICE FIELD THEORY: TWO-DIMENSIONAL
- LATTICE FIELD THEORY: THREE-DIMENSIONAL
- FIELD THEORY: EFFECTIVE ACTION
- GAUGE FIELD THEORY: AXIAL GAUGE
- GAUGE FIELD THEORY: LANDAU GAUGE
- RENORMALIZATION: REGULARIZATION
- APPROXIMATION: MEAN FIELD
- EXPANSION: CLUSTER
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