2017/01/03 by James Lindesay, Lindesay, James
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1701.01332
openalex publication_date 2017/01/03 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
The algebra of the generators for infinitesimal transformations of the\n\Γ=1 over 2 representation of causal spinor fields (Dirac fields)\n\explicitly constructs the Minkowski metric \within the internal\ngroup space as a consequence of non-vanishing commutation relations between\ngenerators that carry a single space-time index. This representation is a\nsubgroup of the set of all of the generators that transform under the group\nGL(4). The sixteen hermitian generators of GL(4) include the three angular\nmomentum spin matrices, a matrix proportional to the Dirac matrix \γ0,\nand 12 additional matrices that have the same number of degrees of freedom as\nSU(3)\×SU(2)\×U(1). In this paper, the construction of linearly\nindependent internal SU(3) and SU(2) local symmetry groups for the causal\nspinor fields is demonstrated to necessarily involve the CKM mixing of three\nsets of the SU(3) eigenstates as related to the SU(2) eigenstates.\n