Abstract
We combine old ideas about exact renormalization-group-flow (RGF) equations with the Vilkovisky–De Witt (VDW) approach to reparametrization invariant effective actions and arrive at a new, exact, gauge-invariant RGF equation. The price to be paid for such a result is that both the action and the RGF equation depend explicitly upon the base point (in field space) needed for the VDW construction. We briefly discuss the complications originating from this fact and possible ways to overcome them.
Highlights
The idea of renormalization, originally introduced to remove infinities from perturbative calculations, has evolved into a powerful tool that helps understanding the global behaviour of quantum and statistical systems under changes of the observation scale[1, 2]
The search for new, non-perturbative methods to handle problems out of the reach of perturbation theory has prompted in recent years a renewed and growing interest [3, 4, 5, 6, 7] in the “old” subject [1, 8] of “exact” renormalization group (RG) equations
In this letter we follow the spirit of Ref. [1, 8], that of direct integration over successive shells of degrees of freedom, and combine this idea with the geometrical approach pioneered by Vilkovisky and De Witt [10, 11] in order to define a gauge-invariant effective action
Summary
The idea of renormalization, originally introduced to remove infinities from perturbative calculations, has evolved into a powerful tool that helps understanding the global behaviour of quantum and statistical systems under changes of the observation scale[1, 2]. The main new results follow as we turn to the case of reparametrization-invariant effective actions a la VDW and their exact RGF equation.
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