The Theory of Infinite Momentum Frames

Infinite momentum frames (IMF) have been first introduced by J. Kogut and L. Susskind ( 1973) in the theory of partons. The concept of infinite momentum frames (IMF) have been developed by R. Dutheil (1984) on the basis of complex rotations group in a pseudo Euclidean space. In the present communication, we re-examine in section 2, the different definitions of IMF proposed by these authors: we criticize the not allowed renormalization of « divergent coordinates » done by J. Kogut and L. Susskind, we abstract the development by R. Dutheil of a two dimensional infinite momentum frame (IMF-2) from considerations on the subluminal and the superluminal Lorentz groups, we criticize the generalization to a four dimensional infinite momentum frame (IMF-4) proposed by R. Dutheil and G. Nibart. In section 3, we study the relativist transformations of two dimensional infinite momentum frames (IMF-2), which correspond to a subluminal Lorentz transformation or a superluminal Lorentz transformation. In section 4, we propose a new mathematical concept of IMF based on isotropic vectors and having any number of dimensions. In section 5, we re-examine the relativist quantum theory in IMF-2 developed by R. Dutheil, we propose a generalization of the Klein, Gordon and Fock equations in IMF-4, and we discuss the generalization by R. Dutheil of the Dirac equations to 4 dimensions.