Chiral-Invariant Perturbation Theory

Charap has found a particular system of pion coordinates leading to chiral-invariant amplitudes, if the usual Feynman rules are applied. It was shown that this system is determined by the condition $\det \left(g_{\mathrm{ik}}\right)=1\mathrm{}$, where $g_{\mathrm{ik}}$ is the metric tensor of the pion space. In the general case the Feynman rules are modified by a counter-term that can be derived from an invariant measure in function space. The counterterm vanishes for $g=1\mathrm{}$.