= Classical-path factorization of a quadratic path integral
{title2=$K(q_f,q_i;T)=N(T)e^{iS[q_c]}$}
For a quadratic <potential energy>, shifting a path to its classical solution leaves an exactly quadratic fluctuation <action> with homogeneous <Dirichlet boundary conditions>. The first variation vanishes by the <Euler-Lagrange equation>. The <Gaussian path integral> prefactor is an inverse square root of a regulated <functional determinant> and does not depend on the endpoints. At conjugate times the ordinary formula must instead be read by distributional continuation.
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