Renormalization group flows from the Hessian geometry of quantum effective actions
Journal of Physics A: Mathematical and Theoretical(2023)
Abstract
We explore a geometric perspective on quantum field theory by considering the configuration space, where all field configurations reside. Employing $n$-particle irreducible effective actions constructed via Legendre transforms of the Schwinger functional, this configuration space can be associated with a Hessian manifold. This allows for various properties and uses of the $n$-particle irreducible effective actions to be re-cast in geometrical terms. In particular, interpreting the two-point source as a regulator, this approach can be readily connected to the functional renormalization group. Renormalization group flows are then understood in terms of geodesics on this Hessian manifold.
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