Renormalization schemes in QED

We discuss the method of dimensional renormalization as applied to quantum electrodynamics. Then we give a general method which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes.     

Renormalization flow of QED

We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral-symmetry-breaking (chiSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the chiSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.     

Intrinsic Loop Regularization and Renormalization in QED

We show how to regularize and renormalize the QED at the one-loop order by means of the intrinsic loop regularization method proposed by the authors. All the results are the same as those derived by means of other regularization methods.     

Renormalization of QED in an external field

The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are given in terms of appropriate Feynman diagrams. The Green function that is used as an electron propagator in each case is discussed in detail. The general renormalization rules for each of the three equations are provided both in a non perturbative way (Dyson relations) and for Feynman diagrams.     

Renormalization of QED with planar binary trees

The Dyson relations between renormalized and bare photon and electron propagators and are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure. Received: 23 March 2000 / Revised version: 24 November 2000 / Published online: 6 April 2001     

Radiative symmetry breaking in supersymmetric models

We propose a scheme where the three relevant physics scales related to the supersymmetry, electroweak, and baryon minus lepton (B−L) breakings are linked together and occur at the TeV scale. The phenomenological implications in the Higgs and leptonic sectors are discussed.     

Gauge symmetry and supersymmetric two-particle problem

An analogy between the removal of nonphysical relative time (or relative energy) in the supersymmetric two-particle problem and the account of local gauge invariance in supersymmetric quantum field theory is discussed. A group of gauge transformations for the Bethe-Salpeter amplitudes is suggested, the invariants of which are the relativistic three-dimensional (quasipotential) wave functions in the Logunov-Tavkhelidze approach. Subsidiary conditions imposed on the Bethe-Salpeter amplitudes in the Todorov approach are shown to be equivalent to appropriate gauge fixing.