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Reposting comment as an answer and expanding. The answer is yes. You can find an exposition in Condensed Matter Field Theory by Altland and Simons, starting on page 134 in the second edition. The troubles come from that spin can't be described with a Hamiltonian that is a function of $q$:s and their conjugate $p$:s. However the more general formulation of ...


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i will have to disagree with some of the answers posted in this question. First, this involves a matter of interpretation of the quantum formalism (and a prevailing "interpretation", the Copenhagen one) Although this interpretation (which i find unsatisfactory and non-physical) may seem prevailing (and indeed it might be), is not because it offers a better ...


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I will not directly answer your question, rather I'll try to make plausible the connexion between QFT and statistical physics. To my mind the mathematical details are somehow obscure and confusing, whereas using the theory is worth a deal, and give interesting results, especially in condensed matter and nuclear matter problems. For more details you can have ...


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You do integrate over all paths in configuration space, but beware : differentiable paths contribute to a measure of 0 in the integral. The real contribution comes from fractal paths of dimension 2 (cf "The Dimension of a Quantum-Mechanical Path" by Abbott and Wise). This "spreading" of the path is the equivalent in path integrals of the Heisenberg ...


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Note that all your integrals are Gaussians in differences of positions at successive instants $(x_k - x_{k-1})$ so implement a change of integration variable from $x_k \longrightarrow (x_k - x_{k-1})$. You will have $N-1$ (straightforward) integrations to perform with $x_0$ and $x_N$ held fixed.



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