One-particle irreducible Wilson action in the gradient flow exact renormalization group formalism | Zendy

Hidenori Sonoda | Zendy; Hiroshi Suzuki | Zendy

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One-particle irreducible Wilson action in the gradient flow exact renormalization group formalism

Author(s) -

Hidenori Sonoda,

Hiroshi Suzuki

Publication year - 2022

Publication title -

progress of theoretical and experimental physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.887

H-Index - 53

ISSN - 2050-3911

DOI - 10.1093/ptep/ptac047

Subject(s) - physics , mathematical physics , legendre transformation , gauge theory , introduction to gauge theory , brst quantization , ansatz , gauge fixing , effective action , renormalization , renormalization group , functional renormalization group , supersymmetric gauge theory , quantum mechanics , quantum electrodynamics , gauge boson , thermodynamics

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.

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