An economical and often physically reasonable way to determine observable quantities in the SB framework is provided by a saddle-point approximation (SPA) to the functional integral. This is equivalent to allowing for a finite expectation value of a Bose field amplitude. Strictly speaking, a finite expectation value of a Bose field operator violates gauge invariance and should not exist. In contrast, a finite saddle-point amplitude of the radial slave boson fields is compatible with Elitzur's theorem.
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