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Note that this auxilliary function does not in general have the property of positivity.
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Strictly speaking, absolute convergence is obtained only for Γ̂ being positive. This can be achieved formally by adding further very weakly coupled N - M channels, the couplings of which can be put to zero after the calculation is done. The corresponding coupling constants should be chosen so small that they do not modify our saddle-point considerations, see below. This is always possible at any, whatever large, but fixed, value of N. Having such regularization in mind, the whole procedure is well-defined.
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We have not indicated unit matrices Î here just treating them as numbers.
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-
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