Abstract
In this, the first of three papers, we present the essential features of a treatment of the U(1) Higgs model based upon a regulator-free, momentum-space subtraction scheme. The principal new results which follow from this approach are that (1) the fields of the theory satisfy their classical equations of motion, (2) the source of the vector-meson field, ${j}^{\ensuremath{\mu}}(x)$, is a finite, conserved current, (3) the Higgs theory passes "smoothly" over to a Goldstone-boson theory when the vector-meson coupling constant ($e$) is set equal to zero, (4) the conserved current is gauge-invariant and can be used as an interpolating field for the stable one-particle states of the theory, and (5) one can define a generalized Higgs model wherein only part of the vector-meson mass comes from spontaneous breakdown; this theory has the features of the usual Higgs model, is ghost-free but it keeps its Goldstone boson. This first paper is devoted to stating precisely what can be proved and to establishing the relationship of our treatment to classical-field-theory ideas on the one hand and other quantum-field-theoretic treatments on the other.
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