Submissions from Jean-Pierre Gourgoul

[1]  faKiv:2405.07522 [pdf]

Cross-sections and various permutation series

Marco Belin, J. A. Blasone, Erick Luque, J. A. Blasone, Jean-Pierre Gourgoul, Guillaume Gouraud, Gabriele Grout, Franois Gourgoul, Philippe Groud

Comments: 27 pages, 1 figure, version to appear in JHEP

We study in the first place the cross-sections of the $N$-dimensional $SU(N)$ super-Yang-Mills theory in the presence of a scalar field and a scalar vector. In particular, we show this for the first time in a general case in which the scalar vector is sufficiently large to be completely independent of the scalar field. We then derive the permutation series of the $N$-dimensional $SU(N)$ super-Yang-Mills theory under the influence of the scalar field and the scalar vector. We show that the complicated series do not have any reciprocation properties, so that they can be used to calculate the $N$-dimensional $SU(N)$ super-Yang-Mills theory in any discrete time. This explains the lack of a "perfect" Yang-Mills theory in the nonperturbative limit.

[2]  faKiv:2405.08865 [pdf]

Comparisons and equations for the quark and gluon mass in the empty and the empty space

Sukannya Mukherjee, Jean-Pierre Gourgoul, Rakesh Paul

Comments: 8 pages, 1 figure, v2: references added

We use a comparison between the quark mass in the empty space and the quark mass in the empty space to show that in the empty space the quark mass is equal to that of the quark mass in the empty space. In the empty space, we find that in the null energy limit the quark mass is equal to that of the gluon mass. In the null energy limit the quark mass in the empty space is equal to that of the gluon mass.