[Show abstract][Hide abstract] ABSTRACT: 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.
Nuclear Physics B 07/2001; 606(1-2-606):231-244. DOI:10.1016/S0550-3213(01)00222-X · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use the Wilson renormalization group (RG) formulation to solve the fine-tuning procedure needed in renormalization schemes breaking the gauge symmetry. To illustrate this method we systematically compute the non-invariant couplings of the ultraviolet action of the SU(2) pure Yang-Mills theory at one-loop order. Comment: 21 pages, Latex epsfig to be published in Nucl.Phys.B
Nuclear Physics B 06/2000; 585(1-2). DOI:10.1016/S0550-3213(00)00381-3 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss a resummed perturbation theory based on the Wilson renormalization group. In this formulation the Wilsonian flowing couplings, which generalize the running coupling, enter directly into the loop expansion. In the case of an asymptotically free theory the flowing coupling is well defined since the infrared Landau pole is absent. We show this property in the case of the OE 3 6 theory. We also extend this formulation to the QED theory and we prove that it is consistent with gauge invariance. Pacs: 11.10.Hi, 11.15.-q, 11.15.Tk. Keywords: Wilson renormalization group, gauge invariance, running coupling. Research supported in part by MURST, Italy 1 Introduction The formulation of quantum field theory based on the Wilson renormalization group [1], which we will call GammaRG, studies the evolution in the infrared cutoff of the Wilsonian effective action S(OE; ; 0 ), where 0 is some ultraviolet cutoff. This functional is obtained by integrating out all degrees of freedom wi...
[Show abstract][Hide abstract] ABSTRACT: We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N = 1 supersymmetric Yang-Mills and show that the local gauge symmetry — broken by the regularization — can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the iterative nature of the procedure. Furthermore, adding matter fields, we reproduce the one-loop supersymmetric chiral anomaly to the second order in the vector field.
Nuclear Physics B 10/1998; 532(1-2-532):473-497. DOI:10.1016/S0550-3213(98)00458-1 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: By using the exact renormalization group formulation we prove perturbatively the Slavnov-Taylor (ST) identities in SU(2) Yang-Mills theory. This results from two properties: locality, i.e. the ST identities are valid if their local part is valid; solvability, i.e. the local part of ST identities is valid if the couplings of the effective action with non-negative dimensions are properly chosen. 1. Introduction A renormalized theory is defined by giving the "relevant part" of the effective action, i.e. its local part involving couplings which have non-negative mass dimension 1 . If the fields have non-zero mass these relevant couplings could be given by the first coefficients of the Taylor expansion of vertex functions around zero momenta. If the fields have zero mass the expansion must be done around some non-vanishing Euclidean subtraction point ¯ 6= 0. For the massless Phi 4 4 theory there are three relevant couplings corresponding to the physical mass, wave function normaliza...
[Show abstract][Hide abstract] ABSTRACT: We extend the Wilson renormalization group (RG) formulation to chiral gauge theories and show that local gauge symmetry can be implemented by a suitable choice of the RG flow boundary conditions. Since the space-time dimension is four, there is no ambiguity in handling the matrix $\g_5$ and left and right fermions are not coupled. As a result the ultraviolet action contains all possible globally chiral invariant interactions. Nevertheless, the correct chiral anomaly is reproduced. Comment: 16 pages, 4 figures, LaTex, uses epsfig, amssymb
Nuclear Physics B 07/1997; 511(1-2). DOI:10.1016/S0550-3213(97)00740-2 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss the relation between the Gell-Mann-Low beta function and the “flowing couplings” of the Wilsonian action SΛ[φ] of the exact renormalization group (RG) at the scale Λ. This relation involves the ultraviolet region of Λ so that the condition of renormalizability is equivalent to the Callan-Symanzik equation. As an illustration, by using the exact RG formulation, we compute the beta function in Yang-Mills theory to one loop (and to two loops for the scalar case). We show that the flowing couplings tend to the running coupling at high frequency, they differ at low frequency and remain finite all the way down to zero frequency. We show also that, by a systematical resummation of higher order corrections, the flowing couplings enter directly into the Feynman diagrams with a scale given by the internal loop momenta.
Nuclear Physics B 01/1997; 483(1-2-483):475-494. DOI:10.1016/S0550-3213(96)00571-8 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that it is possible to formulate a gauge theory starting from a local action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has to require that fields in the UV action and the fields in the effective action are not the same but related by a local field transformation. The few relevant parameters involved in this transformation (six for the $SU(2)$ gauge theory), are perturbatively fixed by the gauge symmetry. Comment: 5 pages, Latex, no figures
Physics Letters B 09/1996; 389(3). DOI:10.1016/S0370-2693(96)01307-X · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the implementation of spontaneously broken symmetries in the Wilson renormalization group formulation. Both for a global and local symmetry, the result is that in perturbation theory one has to tune the boundary conditions for the flow of the relevant couplings. We consider in detail the discrete case and the Abelian Higgs model.
Nuclear Physics B 04/1996; 466(1-2-466):315-334. DOI:10.1016/0550-3213(96)00073-9 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: It is commonly believed that a Yang-Mills theory (and in general a massless theory) with a nonvanishing subtraction point is infrared finite, i.e. the vertex functions at non-exceptional momenta are finite. We give a simple perturbative proof of this fact by using the Wilson renormalization group formulation. The proof requires the control of the singular behaviour of vertex functions only for a restricted class of exceptional configurations of momenta.
Nuclear Physics B 06/1995; 444(3-444):602-616. DOI:10.1016/0550-3213(95)00166-P · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In the exact renormalization-group (RG) flow in the infrared cutoff Λ one needs boundary conditions. In a previous paper on SU(2) Yang-Mills theory we proposed to use the nine physical relevant couplings of the effective action as boundary conditions at the physical point Λ= 0 (these couplings are defined at some non-vanishing subtraction point μ≠ 0). In this paper we show perturbatively that it is possible to appropriately fix these couplings in such a way that the full set of Slavnov-Taylor (ST) identities are satisfied. Three couplings are given by the vector and ghost wave-function normalization and the three-vector coupling at the subtraction point; three of the remaining six are vanishing (e.g. the vector mass) and the others are expressed by irrelevant vertices evaluated at the subtraction point. We follow the method used by Becchi to prove ST identities in the RG framework. There the boundary conditions are given at a non-physical point Λ = Λ′ ≠ 0, so that one avoids the need of a non-vanishing subtraction point.
Nuclear Physics B 03/1995; 437(1-437):163-186. DOI:10.1016/0550-3213(94)00569-Z · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: By using the exact renormalization group formulation we prove perturbatively the Slavnov-Taylor (ST) identities in SU(2) Yang-Mills theory. This results from two properties: {\it locality}, i.e. the ST identities are valid if their local part is valid; {\it solvability}, i.e. the local part of ST identities is valid if the couplings of the effective action with non-negative dimensions are properly chosen. Comment: 9 pages, LaTex, to be published in Phys. Lett. B
Physics Letters B 12/1994; 346(1-2). DOI:10.1016/0370-2693(94)01676-4 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 λ and the boundary conditions for the relevant couplings. The physical theory is obtained at λ = 0. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point λ = λ0 → ∞ but at the physical value λ = 0. As an illustration, we compute the triangle axial anomalies.
Physics Letters B 06/1994; 329(2-3-329):249-258. DOI:10.1016/0370-2693(94)90768-4 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the formulation of the Wilson renormalization group (RG) method for a non-abelian gauge theory. We analyze the simple case of SU(2) and show that the local gauge symmetry can be implemented by suitable boundary conditions for the RG flow. Namely we require that the relevant couplings present in the physical effective action, i.e. the coefficients of the field monomials with dimension not larger than four, are fixed to satisfy the Slavnov-Taylor identities. The full action obtained from the RG equation should then satisfy the same identities. This procedure is similar to the one we used in QED. In this way we avoid the conspicuous fine tuning problem which arises if one gives instead the couplings of the bare lagrangian. To show the practical character of this formulation we deduce the perturbative expansion for the vertex functions in terms of the physical coupling g at the subtraction point μ and perform one-loop calculations. In particular we analyze to this order some ST identities and compute the nine bare couplings. We give a schematic proof of perturbative renormalizability.
Nuclear Physics B 06/1994; 421(2-421):429-455. DOI:10.1016/0550-3213(94)90335-2 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We analyze a formulation of QED based on the Wilson renormalization group. Although the “effective lagrangian” used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's function correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponing counter-terms are generated in the process of fixing the physical conditions.
Nuclear Physics B 04/1994; 418(1-2-418):81-112. DOI:10.1016/0550-3213(94)90239-9 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the “relevant” vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.
Nuclear Physics B 11/1993; 409(2-409):441-464. DOI:10.1016/0550-3213(93)90588-G · 3.93 Impact Factor