Casimir operator dependences of nonperturbative fermionic QCD amplitudes

Abstract

In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes depart from a sole dependence on the SU c (3) quadratic Casimir operator, C 2f , evaluated over the fundamental gauge group representation.Noticed in non-relativistic Quark Models and in a non-perturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other non-perturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of SU c (3). Though numerically sub-leading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the non-perturbative fermonic sector of QCD.

QCD Effective Locality: A Theoretical and Phenomenological Review

“…A , can be permuted without prejudice. One will deal with a 4-point fermionic Green's function (2) as, through more cumbersome expressions, the following structures easily extend to the 2n-point general case (see [14]'s Appendix D, and [15]). Then, two propagators G 1 F (x 1 , y 1 |A) and G 2 F (x 2 , y 2 |A) appear, represented by (4):…”

“…In this quark-current expression (15), the eikonal approximation for the Fradkin field variable u µ (s) consists of a straight line relation connecting the points z and y, u µ (s) = s p µ .…”

“…Dropping L[A], the second and fourth terms on the right hand sides of ( 23), and proceeding to the eikonal replacement of u i (s i ) by s i p i , one immediately recovers the eikonal and quenched results of ( 17) to (20). In the case of higher number of points fermionic Green's functions, additional terms will of course complete the Qa µ and K ab µν functionals in exactly the same way [2,14,15].…”

On How QCD Gauge Invariance Gets Realized in the Context of Effective Locality

“…It cannot show up in the abelian QED case as long hoped (R. P. Feynman, quoted in [12]). It generalizes to the case of 2 -point fermionic Green's functions [13,14]. When truncated to the YM case, the structure found in [6,7] is basically reproduced.…”

“…When truncated to the YM case, the structure found in [6,7] is basically reproduced. Eventually, this result lends itself to a (n analytically continued) Random Matrix exact calculation which takes care of the full integration of thefield dependence and displays the full algebraic dependence of fermionic Green's functions on the (3)-Lie algebra invariants [13,14].…”