The Physical Consequences of a New Version of the Dirac Equation

Abstract

The representation of the 32-part Dirac algebra by a combination of 4-vectors and quaternions allows the Dirac equation to be represented in various simplified forms, including a fully symmetrical version involving all five gamma matrices. The symmetrical version can be used to identify the Dirac spinor wavefunction as containing the square root of a conservation of energy operator whose eigenvalue is zero. This allows us to find explicit expressions for the wavefunction, and for creation and annihilation operators. Immediate physical consequences include Pauli exclusion, the parity-violating single-handedness of massless particles, and the opposite intrinsic parities of fermions and antifermions. The symmetrical equation also leads to more fundamental physical consequences. Mass becomes a ‘fifth’ dimension on a par with the four of space and time, and mass-energy-momentum becomes a five-dimensional operator symmetrical to one representing electromagnetic, strong and weak interactions. Mass can also be structured as a quasi-three-dimensional quantity linked to the existence of three parameters of measurement.