Search results for "Field method"
showing 10 items of 33 documents
Pinch technique for Schwinger-Dyson equations
2007
40 pages, 11 figures.-- ISI Article Identifier: 000245922000041.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0611354
Gluon mass generation in the massless bound-state formalism
2013
We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation its…
Analyzing dynamical gluon mass generation
2007
We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained so…
Bimetric Renormalization Group Flows in Quantum Einstein Gravity
2011
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 the quantum field, and a background metric supplying the coarse graining scale. The central requirement of "background independence" is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first …
Charge radius of the neutrino
2000
Using the pinch technique we construct at one-loop order a neutrino charge radius, which is finite, depends neither on the gauge-fixing parameter nor on the gauge-fixing scheme employed, and is process independent. This definition stems solely from an effective proper photon-neutrino one-loop vertex, with no reference to box or self-energy contributions. The role of the $\mathrm{WW}$ box in this construction is critically examined. In particular it is shown that the exclusion of the effective $\mathrm{WW}$ box from the definition of the neutrino charge radius is not a matter of convention but is in fact dynamically realized when the target fermions are right-handedly polarized. In this way …
Pinch technique self-energies and vertices to all orders in perturbation theory
2003
The all-order construction of the pinch technique gluon self-energy and quark-gluon vertex is presented in detail within the class of linear covariant gauges. The main ingredients in our analysis are the identification of a special Green's function, which serves as a common kernel to all self-energy and vertex diagrams, and the judicious use of the Slavnov-Taylor identity it satisfies. In particular, it is shown that the ghost-Green's functions appearing in this identity capture precisely the result of the pinching action at arbitrary order. By virtue of this observation the construction of the quark-gluon vertex becomes particularly compact. It turns out that the aforementioned ghost-Green…
New Schwinger-Dyson equations for non-Abelian gauge theories
2008
We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the sta…
On dynamical gluon mass generation
2007
The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is so…
Pinch technique at two loops: The case of massless Yang-Mills theories
2000
The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less Yang-Mills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quit…
Charge and magnetic moment of the neutrino in the background field method and in the linear R-xi(L) gauge
1999
We present a computation of the charge and the magnetic moment of the neutrino in the recently developed electro-weak Background Field Method and in the linear $R_{\xi}^L$ gauge. First, we deduce a formal Ward-Takahashi identity which implies the immediate cancellation of the neutrino electric charge. This Ward-Takahashi identity is as simple as that for QED. The computation of the (proper and improper) one loop vertex diagrams contributing to the neutrino electric charge is also presented in an arbitrary gauge, checking in this way the Ward-Takahashi identity previously obtained. Finally, the calculation of the magnetic moment of the neutrino, in the minimal extension of the Standard Model…