One-particle irreducible Wilson action in the gradient flow exact renormalization group formalism
Abstract
We define a one-particle irreducible (1PI) Wilson action in the gradient flow exact renormalization group (GFERG) formalism as the Legendre transform of a Wilson action. We consider quantum electrodynamics in particular, and show that the GFERG flow equation preserves the invariance of the 1PI Wilson action (excluding the gauge-fixing term) under the conventional\/ U(1) gauge transformation. This is in contrast to the invariance of the original Wilson action under a modified U(1) gauge transformation. The global chiral transformation also takes the conventional\/ form for the 1PI Wilson action. Despite the complexity of the GFERG flow equation, the conventional form of the gauge and global chiral transformations may allow us to introduce a non-perturbative Ansatz for gauge and chiral invariant 1PI Wilson actions.