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I don't get how the second-order derivative ##\partial^2 S/\partial x_i \partial x_j## of the phase S arrives here. If one performs a power series expansion of the Hamiltonian around ##\nabla S##, then I do get where the first term ##A## comes from, but then adding higher-order derivatives doesn't seem to introduce this second-order derivative of the phase S (even taking the somewhat

fuzzy footnote into account).

Does anyone who has read this book have an idea?

Thanks in advance.

Pierre

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# I Weinberg Lectures in QM (2013 Ed.), Equation 7.10.15

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