Internal symmetry of hadrons: Finsler geometrical origin

Abstract

The microlocal space of hadronic matter extension has recently been characterized as a Finsler space. This consideration of hadrons extended as composites of constituents can give rise to a dynamical theory of hadrons. The macrospaces, the space-time of common experience (the Minkowski flat space-time) and the Robertson-Walker background space-time of the universe, are found to appear as the “averaged” space-times of the Finsler space that describes the anisotropic nature of the microdomain of hadrons. From the assumed property of the fields of the constituents in the microspace it is possible to find the field (or wave) equations of the particles (or constituents) through the quantization of space-time at small distances (to an order of or less than a fundamental length). If the field (or wave) function is separable in the functions of the coordinates of the underlying manifold and the directional arguments of the Finsler space, then the former part of the field function is found to satisfy the Dirac equation in the Minkowski space-time or in the Robertson-Walker space-time according to the nature of the underlying manifold. In the course of finding a solution for the other part of the field function a relation between the mass of the particle and a parameter in the metric of the space-time has been obtained as a byproduct. This mass relation has cosmological implications and is relevant in the very early stage of the evolution of the universe. In fact, it has been shown elsewhere that the universe might have originated from a nonsingular origin with entropy and matter creations that can account for the observed photon-to-baryon ratio and total particle number of the present universe. The equations in the directional arguments for the constituents in the hadron configuration are found here and give rise to an additional quantum number in the form of an “internal” helicity that can generate the internal symmetry of hadron if one incorporates the arguments of Budini in generating the internal isospin algebra from the conformal reflection group. This consideration can also account for the meson-baryon mass differences.