On the Casimir operator dependences of QCD amplitudes

In eikonal and quenched approximations at least, it is argued that the strong coupling fermionic QCD amplitudes obtained with the help of the newly discovered effective locality property, depart from a dependence on the sole $SU_c(3)$ quadratic Casimir operator, evaluated over the fundamental gauge group representation. This result, in contradistinction with Perturbation Theory, but also with a number of non-perturbative approaches such as the MIT Bag, the Stochastic Vacuum Models, and Lattice simulations, accounts, instead, for the full algebraic content of the rank-2 $SU_c(3)$-Lie algebraComment: New Eq.(6) is more general than the previous one, and is further detailed by Eqs.(7) and (8). Conclusion is a bit more detailed, and the References completed with the titles of article

On a fate of hot quantum field theories

It is argued that for hot quantum fields, the necessary effective perturbation theories may be based on a resummation procedure which, contrarily to the zero temperature case, differs substantially from the one ordinarily in use. Important differences show up in the infrared sector of hot quantum field theories.Comment: Plain TeX-file, 8 pages, no figures. Preprint INLN 2000/1

Proof of a mass singularity free property in high temperature QCD

It is shown that three series of diagrams entering the calculation of some hot $QCD$ process, are mass (or collinear) singularity free, indeed. This generalizes a result which was recently established up to the third non trivial order of (thermal) Perturbation Theory.Comment: 40 pages, 3 figures. to be published in J. Math. Phys. no. 44, 200

On QCD and Effective Locality

In a recent paper it was shown how quark scattering in a quenched, eikonal model led to a momentum-transfer dependent amplitude expressed in terms of Halpern's functional integral; and how the requirement of manifest gauge invariance converted that functional integral into a local integral, capable of being evaluated with precision by a finite set of numerical integrations. We here prove that this property of "effective locality" holds true for all quark processes, without approximation and without exception.Comment: Expanded and Revised in REVTeX 4.1, 14 pages, follow-on work of Eur. Phys. J. C65, pp.395-411 (2010) or arXiv:0903.2644v2 [hep-th

Angular intricacies in hot gauge field theories

It is argued that in hot gauge field theories, "Hard Thermal Loops" leading order calculations call for a definite sequence of angular averages and discontinuity (or Imaginary part prescription) operations, and run otherwise into incorrect results. The ten years old collinear singularity problem of hot $QCD$, provides a striking illustration of that fate.Comment: 14 pages, 1 figur