Proper-time modulus
= Proper-time modulus
{title2=$s$}
The constant mode of the <worldline einbein> is not removed by <gauge transformations> whose parameters vanish at the ends of a fixed interval. This Schwinger proper-time parameter remains integrated over after <gauge fixing>. For $\varphi=(p^2+M^2)/2$, the geometric on-shell proper length is $M\int e\,dt$.