= Coherent-state thermal boundary conditions
{title2=$\psi(\beta)=\zeta\psi(0)$}
The thermal trace closes bosonic coherent-state paths periodically and fermionic coherent-state paths antiperiodically: $\psi(\beta)=\zeta\psi(0)$ and $\bar\psi(\beta)=\zeta\bar\psi(0)$, with $\zeta=1$ for bosons and $-1$ for fermions. The minus sign follows from the <fermionic coherent-state trace>, not from choosing a different Hamiltonian. These boundary conditions determine the allowed <Matsubara frequencies>.
Back to article page
