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.