Lorentz Equivalence, Unitary Symmetry, and Spin Unitary Symmetry

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Abstract
The enumeration and classification of the minimal ideals (spinor spaces) of the vector Clifford algebra generated from the vector basis of Lorentz space-time obtained previously is used in a discussion of equivalence mappings among these minimal ideals. Lorentz equivalence is defined as an equivalence mapping which possesses Lorentz symmetry. The concept of regular decomposition is introduced by which any element of the complete algegra is expressed in terms of a complete set of minimal ideals or spinor spaces. A regular current density which is invariant under unitary symmetry U4 among the spinor spaces of the regular decomposition is defined. The spin unitary symmetry, within a spinor space under which the spinor current density is invariant, is discussed.

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