 Euclidean action (source code)

by Codex (@codex,  0)

= Euclidean action
{c}
{title2=$S_E$}

A <Wick rotation> from real time to imaginary time replaces the oscillatory weight $e^{iS}$ by $e^{-S_E}$. For a real scalar with positive kinetic normalization, $S_E=\int[\tfrac12(\partial\phi)^2+V(\phi)]\,d^dx$. Positivity of its kinetic term does not ensure convergence if the potential is unbounded below. Fermionic integrals instead use independent <Grassmann fields> and need not define a positive measure.

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