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 lightfront 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 twonucleon systems (deuteron, 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. Straigthforward applications to the pion and nucleon form factors and the ρ − π transition are also made. ,0 = − 2η(F 1 − ηF 2 + G 1 /2) + η/2B 6 ,(6.63)The matrix elementsJ 11 ,J 1−1 have the same form as J 11 , J 1−1 , whereasJ 10 ,J 00 differ from J 10 , J 00 by the items containing the nonphysical form factors B 5 , B 6 , B 7 . Other nonphysical form factors B 1−4 and B 8 do not contribute to these matrix elements.The matrix elementsJ λ ′ λ do not satisfy the condition (6.61). SubstitutingJ λ ′ λ in eq.(6.61) instead of J λ ′ λ , we get: ∆ ≡ (1 + 2η)J 11 +J 1−1 − 2 2ηJ 10 −J 00 = −(B 5 + B 7 ) .(6.64)

We develop a new method of solving Bethe-Salpeter (BS) equation in Minkowski space. It is based on projecting the BS equation on the light-front (LF) plane and on the Nakanishi integral representation of the BS amplitude. This method is valid for any kernel given by the irreducible Feynman graphs. For massless ladder exchange, our approach reproduces analytically the Wick-Cutkosky equation. For massive ladder exchange, the numerical results coincide with the ones obtained by Wick rotation.

32 pages, 14 figures, submitted in Phys. Rev. DWithin 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

Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is solved for a kernel given by a sum of ladder and cross-ladder exchanges. The solution of corresponding Light-Front (LF) equation, where we add the time-ordered stretched boxes, is also obtained. Cross-ladder contributions are found to be very large and attractive, whereas the influence of stretched boxes is negligible. Both approaches -BS and LF -give very close results.

The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles [1], is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original BS amplitudes. The numerical solutions for the J = 0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. The stability of the scalar and positronium states without vertex form factor is discussed. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.

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We study the analytic structure of light-front wave functions (LFWFs) and its consequences for hadron form factors using an explicitly Lorentz-invariant formulation of the front form. The normal to the light front is specified by a general null vector ω µ . The LFWFs with definite total angular momentum are eigenstates of a kinematic angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituentsand the light-cone momentum fractions x i = k i ·ω/p·ω multiplied by invariants constructed from the spin matrices, polarization vectors, and ω µ . These properties are illustrated using known nonperturbative eigensolutions of the Wick-Cutkosky model. We analyze the LFWFs introduced by Chung and Coester to describe static and low momentum properties of the nucleons. They correspond to the spin-locking of a quark with the spin of its parent nucleon, together with a positive-energy projection constraint. These extra constraints lead to anomalous dependence of form factors on Q rather than Q 2 . In contrast, the dependence of LFWFs on M 2 0 implies that hadron form factors are analytic functions of Q 2 in agreement with dispersion theory and perturbative QCD. We show that a model incorporating the leading-twist perturbative QCD prediction is consistent with recent data for the ratio of proton Pauli and Dirac form factors.