Algebraic Geometry and Feynman Amplitudes

Abstract

The representation method of obtaining first and second type Landau curves from the Landau criteria is described. The Plucker characteristic analysis of singular curves is outlined and its relationship with the theory of automorphic functions indicated. A differential approach to singularity classification is discussed and a possible extension of the method to obtain asymptotic behaviour is conjectured. A preliminary form of some of the material here presented was the basis of a lecture given by the author at the University of Wales Colloquium in Applied Mathematics, Gregynog, 1969.