Gauge-Invariant Renormalization Group at Finite Temperature

We propose a gauge-invariant version of Wilson Renormalization Group for thermal field theories in real time. The application to the computation of the thermal masses of the gauge bosons in an SU(N) Yang-Mills theory is discussed.Comment: 23 pages, latex2e, 1 EPS figure. The discussions of BRS identities and of the RG kernel have been modified. Final version, to appear on Nucl. Phys.

Exact Symmetries realized on the Renormalized Group Flow

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 as the master equation in the antifield formalism: one may read off the renormalized BRS transformation from the master equation. The Maxwell theory is studied explicitly to see how it works. The renormalized BRS transformation becomes non-local but keeps off-shell nilpotency. Our formalism is applicable for a generic global symmetry. The master equation considered for the chiral symmetry provides us with the continuum analog of the Ginsparg-Wilson relation and the L{\" u}scher's symmetry.Comment: Latex, 10 page

Background field method in the Wilson formulation

A cutoff regularization for a pure Yang-Mills theory is implemented within the background field method keeping explicit the gauge invariance of the effective action. The method has been applied to compute the beta function at one loop order.Comment: LaTex 13 pages, 1 figure; to appear in Nucl.Phys.

Axial anomalies in gauge theory by exact renormalization group method

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff \L and the boundary conditions for the relevant couplings. The physical theory is obtained at \L=0. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point \L=\L_0\to\infty but at the physical value \L=0. As an illustration, we compute the triangle axial anomalies.Comment: 11 pages + 1 appended EPS figure, LaTeX, UPRF 94-39

Gauge invariance and background field formalism in the exact renormalisation group

We discuss gauge symmetry and Ward-Takahashi identities for Wilsonian flows in pure Yang-Mills theories. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated. We examine how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.Comment: version to be published in PL

Polchinski equation, reparameterization invariance and the derivative expansion

The connection between the anomalous dimension and some invariance properties of the fixed point actions within exact RG is explored. As an application, Polchinski equation at next-to-leading order in the derivative expansion is studied. For the Wilson fixed point of the one-component scalar theory in three dimensions we obtain the critical exponents \eta=0.042, \nu=0.622 and \omega=0.754.Comment: 28 pages, LaTeX with psfig, 12 encapsulated PostScript figures. A number wrongly quoted in the abstract correcte

Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature

We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local potential approximation. This approximation reproduces the perturbative results for the screening mass and the pressure up to order g^3, and starts to differ at order g^4. The method allows a smooth extrapolation to the regime where the coupling is not small, very similar to that obtained from a simple self-consistent approximation.Comment: 42 pages, 19 figures; v2: typos corrected and references added, version accepted for publication in Nucl. Phys.