Gauge and Lorentz Covariant Quark Propagator in an Arbitrary Gluon Field

The quark propagator in presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of gluon field and its derivatives. The result is independent of path connecting ends of propagator and leading order result coincides with the exact propagator in the trivial case of vanishing gluon field.Comment: 9 page

Time-domain response of nabla discrete fractional order systems

This paper investigates the time--domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler function. In particular, we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time--domain response; and ii) the dynamic behavior of the zero input response. Finally, one numerical example is provided to show the validity of the theoretical results.Comment: 13 pages, 6 figure