Relativistic wave equations with fractional derivatives and pseudo-differential operators

The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\square^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are local in their nature, the multicomponent equations for arbitrary n>2 are non-local. It is shown, how the representation of generalized algebra of Pauli and Dirac matrices looks like and how these matrices are related to the algebra of SU(n) group. The corresponding representations of the Poincar\'e group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.Comment: 29 pages, Tex. In the corrected version a small bug in cross-references to some equations is removed. Minor text corrections are done and some references are adde

Kinematics of deep inelastic scattering in the covariant approach

We study the kinematics of deep inelastic scattering corresponding to the rotationally symmetric distribution of quark momenta in the nucleon rest frame. It is shown that the rotational symmetry together with Lorentz invariance can impose constraints on the quark intrinsic momenta. Obtained constraints are discussed and compared with the available experimental data

Quark orbital angular momentum: can we learn about it from GPDs and TMDs?

It is known how to access information on quark orbital angular momentum from generalized parton distribution functions, in a certain specified framework. It is intuitively expected, that such information can be accessed also through transverse momentum dependent distribution functions, but not known how. Now quark models provide promising hints. Recent results are reviewed.Comment: proceeding of the "4th Workshop on Exclusive Reactions at High Momentum Transfer," 18-21 May 2010, Jefferson La

Parton distribution functions and quark orbital motion

Covariant version of the quark-parton model is studied. Dependence of the structure functions and parton distributions on the 3D quark intrinsic motion is discussed. The important role of the quark orbital momentum, which is a particular case of intrinsic motion, appears as a direct consequence of the covariant description. Effect of orbital motion is substantial especially for polarized structure functions. At the same time, the procedure for obtaining the quark momentum distributions of polarized quarks from the combination of polarized and unpolarized structure functions is suggested.Comment: 17 pages, 2 figures, 1 table. Paper is accepted for publication in Eur.Phys.J.