Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model

We present a coherent and operational strategy to calculate, in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that, once the renormalization conditions are properly taken into account, the form factors do not depend on the regularization scale, when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.Comment: 22 pages, 16 figure

Systematic renormalization scheme in light-front dynamics with Fock space truncation

Within the framework of the covariant formulation of light-front dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.Comment: 32 pages, 14 figures, submitted in Phys. Rev.

Recent developments in light-front dynamics

Recent results on relativistic few body systems, obtained in the framework of light-front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero-range interaction; many-body contributions.Comment: 5 pages, 4 figures, to appear in the proceedings of the 19th European Conference on Few-Body Problems in Physics, Groningen, The Netherlands, August 23-27, 200

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space

Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.Comment: 24 pages, 16 figure

Bethe-Salpeter scattering amplitude in Minkowski space

The off-mass shell scattering amplitude, satisfying the Bethe-Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.Comment: 9 pages, 4 figures, 2 tables, to be published in Phys. Lett.