Clifford Periodicity from Finite Groups
نویسندگان
چکیده
We deduce the periodicity 8 for the type of Pin and Spin representations of the orthogonal groups O(n) from simple combinatorial properties of the finite Clifford groups generated by the gamma matrices. We also include the case of arbitrary signature O(p, q). The changes in the type of representation can be seen as a rotation in the complex plane. The essential result is that adding a (+) dimension performs a rotation by π/4 in the counter clock-wise sense, but for each (−) sign in the metric, the rotation is clockwise. Permanent address Departamento de F́ısica Teorica, Facultad de Ciencias. Universidad de Zaragoza, E-50009 Zaragoza, Spain. Email: [email protected] [email protected]
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