Euclidean worldline path integral
= Euclidean worldline path integral
{c}
A thermal <path integral> represents the <canonical partition function> by paths periodic in Euclidean time of circumference $\beta$. For $H=p^2/2+V(x)$, its formal action is $S_E[x]=\int_0^\beta(\dot x^2/2+V(x))\,d\tau$. The <periodic boundary condition> results from taking the trace of the evolution kernel. The continuum measure requires a regularization and normalization; finite-dimensional measures make both choices explicit.