J.-F. Mathiot

Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems

Abstract The wave function of a composite system is defined in relativity on a space–time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane ω · x =0, where ω is an arbitrary four-vector with ω 2 =0. The standard non-covariant approach is recovered as a particular case for ω=(1, 0, 0,−1) . Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review. The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented. The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, 1 2 and 1 systems. The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron and scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straightforward applications to the pion and nucleon form factors and the ρ −π transition are also made.

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 nonperturbative 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.

Interplay of three-body interactions in the EOS of nuclear matter

Abstract The equation of state of symmetric nuclear matter has been investigated within Brueckner approach adopting the charge-dependent Argonne V 18 two-body force plus a microscopic three-body force based on a meson-exchange model. The effects on the equation of state of the individual processes giving rise to the three-body force are explored up to high baryonic density. It is found that the major role is played by the competition between the strongly repulsive ( σ , ω )-exchange term with virtual nucleon–antinucleon excitation and the large attractive contribution due to ( σ , ω ) exchange with N ∗ (1440) resonance excitation. The net result is a repulsive term which shifts the saturation density corresponding to the only two-body force much closer to the empirical value, while keeping constant the saturation energy per particle. The contribution from ( π , ρ )-exchange 3BF is shown to be attractive and rather small. The analysis of the separate three-body force contributions allows to make a comparison with the prediction of Dirac–Brueckner approach which is supposed to incorporate via the dressed Dirac spinors the same virtual nucleon–antinucleon excitations as in the present three-body force. The numerical results suggest that the three-body force components missing from the Dirac–Brueckner approach are not negligible, especially at high density. The calculation of the nuclear mean field and the effective mass shows that the three-body force affects to a limited extent such properties.

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.

Isovector meson-exchange currents in the light-front dynamics

In the light-front dynamics, there is no pair term that plays the role of the dominant isovector pion exchange current. This current gives rise to the large and experimentally observed contribution to the deuteron electrodisintegration cross-section near threshold for pseudo-scalar πNN coupling. We show analytically that in leading 1m order the amplitude in the light-front dynamics coincides, however, with the one given by the pair term. At high Q2, it consists of two equal parts. One comes from extra components of the deuteron and final state relativistic wave functions. The other results from the contact NNπγ interaction which appears in the light-front dynamics. This provides a transparent link between relativistic and non-relativistic approaches.

Taylor-Lagrange renormalization scheme: Application to light-front dynamics

The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagranges formulas, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show, in particular, how rotational invariance is preserved in this scheme.

Renormalized Non-Perturbative Scalar and Fermion Models in Covariant Light-Front Dynamics

Abstract.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 explicit dependence of our formalism on the orientation of the light front, defined by a light-like four-vector ω, is essential in order to analyze the structure of the counterterms needed to renormalize the theory. We illustrate our framework for scalar and fermion models.

A density-dependent effective interaction for relativistic Hartree-Fock calculations

Abstract We present a general method to derive density-dependent effective interactions to be used in the relativistic Hartree-Fock approximation. In the non-relativistic limit (i.e. at low density), this method is identical to the usual variational ansatz with a two-body correlation function whose range is used as a variational parameter. At normal nuclear matter density, it provides a useful prescription to fit relativistic Brueckner-Hartree-Fock calculations. It provides in particular a physical way to deal with the zero-range pieces of π and ϱ interactions in the medium. We apply our method to infinite symmetric nuclear matter. This effective interaction is also particularly well suited for calculations in finite nuclei.

Aspects of fine-tuning of the Higgs mass within finite field theories

We reanalyze the perturbative radiative corrections to the Higgs mass within the Standard Model in the light of the Taylor-Lagrange renormalization scheme. This scheme naturally leads to completely finite corrections, depending on an arbitrary scale. The formulation avoids very large individual corrections to the Higgs mass. This illustrates the fact that the so-called fine-tuning problem in the Standard Model is just an artifact of the regularization scheme. It should therefore not lead to any physical interpretation in terms of the energy scale at which new physics should show up, nor in terms of a new symmetry. We analyze the intrinsic physical scales relevant for the description of these radiative corrections.