QUATERNION QUANTUM-MECHANICS AS THE DESCRIPTION OF TACHYONS AND QUARKS

Physics is not symmetric with respect to time and space. To obtain symmetry between space and time, it is necessary to consider the new part of physics-the space-like physics in which the evolution takes place in space and the state of system is defined on the time axis. It is shown that the corresponding Quantum Mechanics must be based on the field of quaternions instead of the field of complex numbers. Equations analogical to the usual electrodynamics are found. In these equations the Yang-Mills field plays the role of the photon field. Then the corresponding hypothetical particles are interpreted as quarks. In this interpretation the symmetry between space and time is connected with the quark-lepton symmetry. © 1979 Academia, Publishing House of the Czechoslovak Academy of Sciences.