  In response to a recent work by Mandula, we investigate whether there are any
ambiguities in the expression for the pion mass resulting from multiple chiral
symmetries. If the conserved current for Ginsparg Wilson chiral symmetries is
calculated in the usual way, different expressions of the chiral symmetry lead
to different currents. This implies an ambiguity in the definition of the pion
and pion decay constant for all Ginsparg-Wilson expressions of the Dirac
operator, including the overlap operator on the lattice (although all these
currents would have the same continuum limit). We use a renormalisation group
mapping procedure to consider local chiral symmetry transformations for a
continuum Ginsparg-Wilson "Dirac-operator." We find that this naturally leads
to an expression for the conserved current which is independent of which of the
Ginsparg-Wilson symmetries is chosen. We recover the standard expressions for
the massive Dirac operator, propagator, and chiral condensate. Our main
conclusion is that, when the currents are properly constructed and consistently
applied, no observable depends on which Mandula symmetry is used; at least in
these continuum Ginsparg-Wilson theories. We will consider whether the same
argument applies to lattice theories in a subsequent paper.
