why when we want to evaluate a functional determinant we use the expansion near $ t=0$ for the partition function $ \sum_{n}e^{-tE_{n}} \sim \sum_{n} a_{n} (t)t^{n} $ instead of just using the semiclassical partition function ?? $ \iint _{\Gamma}dx dpe^{-tp^{2}-tV(x)} $ which is just easier to handle with ? fo rexamplelin almost all papers i have seen this asymptotic approximation for the partition function near $ t=0$ although coefficients are hard to evaluate.
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