ar X iv : h ep - p h / 95 05 37 3 v 1 2 4 M ay 1 99 5 FORMS OF RELATIVISTIC DYNAMICS , CURRENT OPERATORS AND DEEP INELASTIC LEPTON - NUCLEON SCATTERING

The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point form. In particular, the parton model which is the consequence of the impulse approximation in the front form is incompatible with Lorentz invari-ance, P invariance and T invariance. The results for deep inelastic scattering based on the impulse approximation in the point form give natural qualitative explanation of the fact that the values given by the parton model sum rules exceed the corresponding experimental quantities. The title of this section repeats the title of paper 1 in which the notion of the forms of relativistic dynamics was introduced for the first time. In quantum field theory the four-momentum operatorsˆP µ (µ = 0, ...3) and the representation generators of the Lorentz groupˆM µν = − ˆ M νµ (µ, ν = 0, ...3) are given by integrals from the energy-momentum and angular momentum tensors over a space-like (or light-like) hypersurface. Dirac 1 related the different choices of the hypersurfaces to the different forms of relativistic dynamics. By definition, the description in the point form implies that the operatorsˆM µν are the same as for noninteracting particles, and thus interaction terms can be present only in the operatorsˆP. If some operator is the same as for the noninteracting system, we shall write this operator without " a hat ". Therefore, the point form is defined by the conditionˆM µν = M µν and in the general casê P µ = P µ for all µ. The description in the instant form implies that the operators of ordinary momentum and angular momentum do not depend on interactions, i. M 12)) and therefore interactions may be present only inˆP 0 and the generators of the Lorentz boostsˆN = (ˆ M 01 , ˆ M 02 , ˆ M 03). In the front form with the marked z axis we introduce the + and-components of the 4-vectors as p + = (p 0 + p z)/ √ 2, p − = (p 0 − p z)/ √ 2. Then we require that the 1