  In this paper we reanalyze the electroweak chiral Lagrangian with particular
focus on two issues related to gauge invariance. Our analysis is based on a
manifestly gauge-invariant approach that we introduced recently. It deals with
gauge-invariant Green's functions and provides a method to evaluate the
corresponding generating functional without fixing the gauge. First we show,
for the case where no fermions are included in the effective Lagrangian, that
the set of low-energy constants currently used in the literature is redundant.
In particular, by employing the equations of motion for the gauge fields one
can choose to remove two low-energy constants which contribute to the
self-energies of the gauge bosons. If fermions are included in the effective
field theory analysis the situation is more involved. Even in this case,
however, these contributions to the self-energies of the gauge bosons can be
removed. The relation of this result to the experimentally determined values
for the oblique parameters S, T, and U is discussed. In the second part of the
paper we consider the matching relation between a full and an effective theory.
We show how the low-energy constants of the effective Lagrangian can be
determined by matching gauge-invariant Green's functions in both theories. As
an application we explicitly evaluate the low-energy constants for the standard
model with a heavy Higgs boson. The matching at the one-loop level and at
next-to-leading order in the low-energy expansion is performed employing
functional methods.
