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 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)

Relativistic quantum mechanics: a Dirac's point-form inspired approach

“…In the present case however, it will turn out to vanish, very much like in front-form approaches where P µ int is proportional to a 4-vector ω µ with the property ω 2 = 0 (see for instance Ref. [15]). …”

“…(16) is obtained but with u replaced by the orientation of the front, n (see for instance Ref. [15]). These similarities may be useful to understand the relationship between different approaches.…”

Many-body Fock sectors in Wick–Cutkosky model

“…This results in natural formulation of the concept of a relativistic wave function in terms of the LF Fock expansion at fixed LF time, which is usually put to zero for a stationary state: ω·x = 0. The null four-vector ω (ω 2 = 0) determines the orientation of the LF plane; the freedom to choose ω provides an explicitly covariant formulation of LF quantization [10]. The Fock decomposition has the form:…”

Frame dependence of the pair contribution to the pion electromagnetic form factor in a light-front approach

“…This was seen in schematic covariant models for spin-zero composite systems [3,4,5]. However, even in the Drell-Yan frame the pair term is present in j + for spin-one systems and is necessary to keep the rotational properties of the matrix element of the current [6,7].To avoid the difficulties associated with the rotational properties of the impulse approximation some physically motivated schemes to extract form factors from the current were used [8,9,10]. In another approach, free of these ambiguities [11], the plus component of the momentum transfer is non zero while the transverse momentum transfer vanishes in the Breit frame.…”