This gauge-invariant quantity will serve our purpose to derive the off-shell nilpotent (anti)BRST transformations for [theta] variable [27-29].
Furthermore, we point out that the dynamical variables r, [p.sub.r], and [p.sub.[theta]] are also gauge-invariant as one can see from (2).
We note that the gauge-invariant (first-order) Lagrangian (1) can be generalized to super Lagrangian in terms of the supervariables (13) and (19) as
(i) This result is obviously gauge-independent, that is, gauge-invariant. It cannot show up in the abelian QED case as long hoped (R.
With the functional L[A] being local and fully gauge-invariant, one may consider the case of a fermionic 2-point Green's function generalization to a higher number of points being trivial.
So the matrix [S.sub.jj] is triply degenerate at the point, which, as explained at the beginning of this section, is the criterion for locating the "centre" of a topological configuration in a gauge-invariant description.
while the symmetric matrix [E.sub.ji] is gauge-invariant and is the symmetric square-root of the metric [g.sub.ij].
The three gauge degrees of freedom reside in R and the six gauge-invariant degrees of freedom reside in E.
It should again be stressed here that the gauge-invariant variables (21) commute with the sole first constraint (Gauss law), showing in this way that these fields are physical variables.
To do this, we will use the gauge-invariant scalar potential which is given by expression (19).
Thus, literal interpretations render the theory indeterministic.(10) Of course, if we supplement this account of the ontology of the theory with an account of measurement which implies that its observable quantities are gauge-invariant, then the indeterminism will not interfere with our ability to derive determinate predictions from the theory.
In this simply gauge-invariant case, our theory will be deterministic.