How to generate families of spinors

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Abstract
Using a technique [Mankoč Borštnik et al., J. Math. Phys. 43, 5782 (2002)] to construct a basis for spinors and “families” of spinors in terms of Clifford algebra objects, we define other Clifford algebra objects, which transform the state of one “family” of spinors into the state of another “family” of spinors, changing nothing but the “family” number. The proposed transformation works—as does the technique—for all dimensions and any signature and might open a path to understanding families of quarks and leptons [Mankoč Borštnik, Phys. Lett. B 292, 25 (1992); J. Math. Phys. 34, 3731 (1993); Int. J. Theor. Phys. 40, 315 (2001); Borštnik Bračič and Mankoč Borštnik, hep-ph/0301029].

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