= Coherent-state time slicing
Insert the <coherent-state resolution of identity> between short-time evolution operators. For a normally ordered <Hamiltonian>, the kernel uses the next bra label and current ket label: $\langle\psi_{j+1}|e^{-\epsilon H}|\psi_j\rangle=\exp(\bar\psi_{j+1}\psi_j-\epsilon H(\bar\psi_{j+1},\psi_j)+O(\epsilon^2))$. Together with the Gaussian measure this yields the first-order derivative term $\bar\psi\partial_\tau\psi$. The adjacent-label prescription retains operator ordering information that a formal continuum expression alone can hide.
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