Vacuum projection by imaginary time
= Vacuum projection by imaginary time
{title2=$e^{-TH}|n\rangle=e^{-TE_n}|n\rangle$}
Long imaginary-time evolution multiplies an <energy eigenstate> by $e^{-TE_n}$. After normalization it projects onto the lowest energy component with nonzero initial overlap, or onto the lowest-energy subspace if the vacuum is degenerate. This provides vacuum boundary conditions for a <path integral> and is related to the <Feynman i-epsilon prescription>.