Symmetry Breaking And The Nilpotent Dirac Equation
- Department of Physics, University of Liverpool, Oliver Lodge Laboratory, Oxford Street, Liverpool, L69 7ZE (United Kingdom)
A multivariate 4-vector representation for space-time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak interactions, by associating their respective charges with vector, scalar and pseudoscalar operators, leading directly to the SU(3) x SU(2)L x U(1) symmetry, and to particle structures and mass-generating states. In addition, the nilpotent Dirac equation has just three solutions for spherically-symmetric distance-dependent potentials, and these correspond once again to those that would be expected for the three interactions: linear for the strong interaction; inverse linear for the electromagnetic; and a harmonic oscillator-type solution, which can be equated with the dipolar annihilation and creation mechanisms of the weak interaction.
- OSTI ID:
- 20632681
- Journal Information:
- AIP Conference Proceedings, Vol. 718, Issue 1; Conference: CASYS'03: 6. international conference on computing anticipatory systems, Liege (Belgium), 11-16 Aug 2003; Other Information: DOI: 10.1063/1.1787315; (c) 2004 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ANNIHILATION
DIRAC EQUATION
FERMIONS
HARMONIC OSCILLATORS
MATHEMATICAL SOLUTIONS
MULTIVARIATE ANALYSIS
PARTICLE STRUCTURE
POTENTIALS
REST MASS
SCALARS
SPACE-TIME
STANDARD MODEL
STRONG INTERACTIONS
SU-2 GROUPS
SU-3 GROUPS
SYMMETRY BREAKING
U-1 GROUPS
VECTORS
WEAK INTERACTIONS