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

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

Nonlocal Effective Field Equations for Quantum Cosmology

The possibility that the strength of gravitational interactions might slowly increase with distance, is explored by formulating a set of effective field equations, which incorporate the gravitational, vacuum-polarization induced, running of Newton's constant $G$. The resulting long distance (or large time) behaviour depends on only one adjustable parameter $\xi$, and the implications for the Robertson-Walker universe are calculated, predicting an accelerated power-law expansion at later times $t \sim \xi \sim 1/H$.Comment: 9 page

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.

Transverse momentum dependent distribution functions in a covariant parton model approach with quark orbital motion

Transverse parton momentum dependent distribution functions (TMDs) of the nucleon are studied in a covariant model, which describes the intrinsic motion of partons in terms of a covariant momentum distribution. The consistency of the approach is demonstrated, and model relations among TMDs are studied. As a byproduct it is shown how the approach allows to formulate the non-relativistic limit.Comment: 16 page