The consequences of the assumption of invariance of a spinor theory under local automorphism transformations of the Clifford algebra basis elements are explored. This invariance is equivalent to allowing the orthonormal basis spinors of the spinor space to be chosen arbitrarily at each point in space-time and is analogous to the situation in general relativity where the orthonormal basis vectors of the tangent space are allowed to be chosen arbitrarily at each point in space-time. This invariance then dictates that the Clifford algebra generators be functions of space-time and is implemented by introducing new fields, the drehbeins ("spin legs"), which are somewhat akin to the vielbeins introduced in general relativity to invoke the concept of local Lorentz invariance. However, in contrast to general relativity, the covariant derivatives of the Clifford algebra generators do not vanish. The dynamical variables of the theory are then the spinors, the gauge fields of the automorphism group, and the drehbeins. The invariant Lagrangian density and the concomitant field equations for this theory are discussed. Interestingly, the "kinetic" Lagrangian density term for the drehbein fields induces a gauge invariant mass term for the gauge fields. This constitutes a new mass generation mechanism, of different character and complementary to the familiar Higgs mechanism. Although the idea of local automorphism invariance is a natural generalization of the principle of equivalence, herein attention is restricted to the case of nondynamic flat space-time.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics