# Arefeva, Slavnov, Faddeev ## Generating functional for the S matrix in gauge-invariant theories \[Links: [DOI](https://link.springer.com/article/10.1007/BF01038094)\] \[Abstract: An expression is obtained for the generating functional of the elements of the S matrix. It is shown that in electrodynamics and in a Yang-Mills theory all the ultraviolet divergences can be eliminated by charge renormalization. In the formalism, gauge-dependent counter terms do not arise at all.\] # Hawking ## Black hole explosions \[Links: [Inspire](https://doi.org/10.1038/248030a0)\] ## Refs - [[0304 Hawking radiation]] # 't Hooft ## A Planar Diagram Theory for Strong Interactions \[Links: [Inspire](https://inspirehep.net/literature/80491)\] \[Abstract: A gauge theory with colour gauge group $U(N)$ and quarks having a colour index running from one to $N$ is considered in the limit $N\to\infty$, $g^2 N$ fixed. It is shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in $1/ N$ is identical to that of the dual models, such that the number $1/ N$ corresponds to the dual coupling constant. For hadrons $N$ is probably equal to three. A mathematical framework is proposed to link these concepts of planar diagrams with the functional integrals of Gervais, Sakita and Mandelstam for the dual string.\]