Related papers: BRS Symmetry, the Quantum Master Equation, and the…
Using the average action defined with a continuum analog of the block spin transformation, we show the presence of gauge symmetry along the Wilsonian renormalization group flow. As a reflection of the gauge symmetry, the average action…
We show that the Quantum Master Equation and the Wilsonian renormalization group (RG) flow equation can be combined such that for the continuum effective action, quantum BRST invariance is not broken by the presence of an effective…
Using the Pauli-Villars regularization, we make a perturbative analysis of the quantum master equation (QME), $\Sigma =0$, for the Wilsonian effective action. It is found that the QME for the UV action determines whether exact gauge…
We show that symmetries are preserved exactly along the (Wilsonian) renormalization group flow, though the IR cutoff deforms concrete forms of the transformations. For a gauge theory the cutoff dependent Ward-Takahashi identity is written…
Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the…
The standard flow equation for the effective average action can be derived from a Legendre transform of Polchinski's exact renormalization group equation. However, the latter is not well adapted for finding fixed-points with non-zero…
We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can…
The formulation of an exact functional renormalization group equation for Quantum Einstein Gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of…
In a recent paper, with Drago and Pinamonti we have introduced a Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using the algebraic approach to perturbative QFT. The equation governs the flow of the effective…
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 non linear way. The Wilsonian action and the average effective action are then simply…
We present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff dependent global symmetries along the Wilsonian renormalization group (RG) flow. For…
We construct a new version of the effective average action together with its flow equation. The construction entails in particular the consistency of fluctuation field and background field equations of motion, even for finite…
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions,…
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\Gamma_k$. The ordinary effective action $\Gamma_0$ can be obtained by integrating the flow equation from…
We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative…
These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization…
In this paper, inspired by the Costello's seminal work, we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and…
It is shown that exact renormalization group (RG) equations (including rescaling and field-renormalization) for respectively the scale-dependent full action $S[\phi,t]$ and the scale-dependent full effective action $\Gamma[\Phi,t]$ --in…
We formulate quantum electrodynamics on the basis of gauge (or BRST) covariant diffusion equations of fields. This is a particular example of the gradient flow exact renormalization group (GFERG). The resulting Wilson action fulfills a…
We present a functional renormalization group flow for many-fermion lattice models into phases with broken spin-rotational symmetry. The flow is expressed purely in terms of fermionic vertex functions. The symmetry breaking is seeded by a…