Abstract:
The results of Part I are generalized to the non-Abelian ease. By analogy with
conformal QED, in which interaction with a matter field is realized by means of
a four-vector potential that transforms in accordance with a direct sum of two
nonprincipal representations, the first step in the present paper is the construction
of a new formulation of quantum eleetrodynamics, in which the four-vector
potential is regarded as an independent variable. Although the potential as a whole
transforms in accordance with a principal representation, the corresponding
conformally invariant two-point functions have a nonzero transverse part, and
the Lagrangian is nondegenerate. In the non-Abelian case, one manifestly
conformally invariant gauge condition is found, and the corresponding functional
determinant is calculated. It is shown that in the gauge-invariant sector this
theory is equivalent to the ordinary theory with conformally noninvariant gauge
condition. A local effective Lagrangian is constructed, the Faddeev–Popov “ghost”
fields having in this case scale dimension zero. It is shown that this effective
Lagrangian has a residual global supersymmetry of Becchi–Rouet–Stora type.
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