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Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.
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Almost Gaussian integral over complex vectors of scalars [closed]
I know that the Gaussian integral over complex vectors $\mathbf{u}=(u_1,\dots u_N)$, where $u_i$ are complex valued, is
$$\int \mathcal{D}[\mathbf{u}^*,\mathbf{u}] e^{-\mathbf{u}^* A\mathbf{u}+\mathbf …