Non-local fields in the Z(2) Higgs model: The global gauge symmetry breaking and the confinement problem. (English) Zbl 0615.46070
A method is proposed in lattice gauge models with matter fields which allows to study gauge superselection sectors on the level of the classical statistical system associated to the lattice quantum field theory. The method consists of extending the Gibbs state from the classical observables (continuous gauge invariant functionals) to a certain algebra of (in general non-measurable) functionals called non- local fields. The infrared asymptotics of a non-local field determines the sector to which it belongs. The archetype of non-local fields is the matter field in a complete gauge fixing like Dirac’s gauge invariant electron field.
In the Z(2) Higgs model the following results were obtained using non- local fields and convergent cluster expansions. If both the gauge coupling and the hopping parameter are small there exists locally gauge invariant finite energy states with charge -1. These states form a sector which does not contain translation invariant states. This charged sector is equivalent to the one constructed by Fredenhagen and Marcu. For large gauge coupling and small hopping parameter all non-local fields of charge -1 turned out to create the zero norm state (partial proof of confinement). For large hopping parameter non-local fields of charge -1 do create non-zero states but these states belong to the vacuum sector. The discrepancy between the unobservable bare charge defined by the charge of the field and the observable charge can be interpreted as screening. The Higgs field in an appropriate gauge fixing has non-zero expectation value in this region. The latter result shows in particular that a study of global gauge symmetry breaking in a gauge fixed formalism has no a priori relevance to physics. This is a non-local system which can produce symmetry breaking where there is no phase transition at all in terms of observables.
In the Z(2) Higgs model the following results were obtained using non- local fields and convergent cluster expansions. If both the gauge coupling and the hopping parameter are small there exists locally gauge invariant finite energy states with charge -1. These states form a sector which does not contain translation invariant states. This charged sector is equivalent to the one constructed by Fredenhagen and Marcu. For large gauge coupling and small hopping parameter all non-local fields of charge -1 turned out to create the zero norm state (partial proof of confinement). For large hopping parameter non-local fields of charge -1 do create non-zero states but these states belong to the vacuum sector. The discrepancy between the unobservable bare charge defined by the charge of the field and the observable charge can be interpreted as screening. The Higgs field in an appropriate gauge fixing has non-zero expectation value in this region. The latter result shows in particular that a study of global gauge symmetry breaking in a gauge fixed formalism has no a priori relevance to physics. This is a non-local system which can produce symmetry breaking where there is no phase transition at all in terms of observables.
Keywords:
lattice gauge models; matter fields; gauge superselection sectors; lattice quantum field theory; Gibbs state; non-local fields; infrared asymptotics; Z(2) Higgs model; hopping parameter; confinement; global gauge symmetry breakingReferences:
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