Extended Spinor Structure and Exotic Spinor Field in <Poincare>^^^- Gauge Theory of Gravity : Particles and Fields

概要

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In <Poincare>^^^- gauge theory of gravity developed previously, we show that there is a structure, which is an extension of spinor structure, on the space-time manifold. An internal <Poincare>^^^- gauge transformation induces a Poincare transformation on the tangent affine space at each point of the space-time. Corresponding to the extended spinor structure, a spinor field φ having the "intrinsic" energy-momentum (=the quantum number associated with the internal translation) P_k=Kγ_k(1-sγ_5) is defined. We give an action I^M of φ on the Minkowski space-time, which leads to the Klein-Gordon equation. The action I^M is invariant both under the "internal <Poincare>^^^-" and the "Poincare coordinate" transformations, and there are four conserved physical quantities correspondingly. They are the "intrinsic" and canonical energy-momenta and spin and Orbital angular momenta. The "Poincare coordinate" transformation can be regarded as a kind of internal transformation. For the interacting system of φ and <Poincare>^^^- gauge fields, we have only two conserved quantities: one energy-momentum and one angular momentum. The "intrinsic" and canonical energy-momenta (the spin and orbital angular momenta) of the field φ are transformed into each other through the <Poincare>^^^- gauge interaction. A brief comment on the second quantization of the free φ field on the Minkowski space-time is given.
理論物理学刊行会の論文
1989-10-25