Abstract
We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special nonlinear way. The Wilsonian action and the average effective action are then simply related by a Legendre transformation up to a trivial quadratic form. An exact mapping between canonical and non-canonical theories is obtained as well as the relations between their flows. An application to the theory of liquids is sketched.
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