Quaternionic Formulation of Dirac Theory in Special and General Relativity

概要

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It is shown that Dirac theory can be formulated also in the quaternion form at the Lagrangian level. Crucial to our formulation is that a spinor-quaternion, which may be regarded as 2×2 matrix-valued complex fields, is decomposed into left ideals in a Lorentz invariant manner. The new formalism is applied to gauge theories. Assuming that not only the space-time symmetry but also the internal symmetry are described by Hamilton's quaternions, we are led to the previous algebraic formulation of the standard SU(3)×SU(2)_L×SU(2)_R×U(1) theory with the required family structure of quarks and leptons including spin. The gauge principle with respect to the space-time symmetry, on the other hand, naturally leads to the quaternionic formulation of the Poincare gauge theory for spin-1/2 particles. The most general gravitational Lagrangian of Hayashi is presented in the quaternion form without referring to the principle of irreducibility.
理論物理学刊行会の論文
1983-12-25