Effective Action and Cluster Properties of the Abelian Higgs Model

Balaban, Tadeusz; Imbrie, John Z.; Jaffe, Arthur M.

doi:10.1007/BF01225038

Effective Action and Cluster Properties of the Abelian Higgs Model

Tadeusz Balaban
(
- Northeastern U. and
- Harvard U.
)
,
John Z. Imbrie
(
- Northeastern U. and
- Harvard U.
)
,
Arthur M. Jaffe
(
- Northeastern U. and
- Harvard U.
)

Apr 21, 1987

81 pages

Published in:

Commun.Math.Phys. 114 (1988) 257

DOI:

10.1007/BF01225038

Report number:

HUTMP-87/B200

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Abstract: (Springer)

We continue our program to establish the Higgs mechanism and mass gap for the abelian Higgs model in two and three dimensions. We develop a multiscale cluster expansion for the high frequency modes of the theory, within a framework of iterated renormalization group transformations. The expansions yield decoupling properties needed for a proof of exponential decay of correlations. The result of this analysis is a gauge invariant unit lattice theory with a deep Higgs potential of the shape required to exhibit the Higgs mechanism.

GAUGE FIELD THEORY: U(1)
MODEL: HIGGS
FIELD THEORY: TWO-DIMENSIONAL
FIELD THEORY: THREE-DIMENSIONAL
LATTICE FIELD THEORY: EFFECTIVE ACTION
MASS
RENORMALIZATION GROUP
EXPANSION: CLUSTER
EXPANSION: MAYER
decoupling