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This operator represents the transformation that inverts the 5-axis and leaves the 0, 1, 2, 3-axes unaffected, perhaps interpretable as charge-conjugation C.
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These actions are equivalent to four-dimensional Dirac matrices γµ, σµv, etc..
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If it anticommutes with , then it can represent the transformation that inverts the 5-axis and leaves the 0, 1, 2,3,4-axes unaffected; if it anticommutes with and , then it can represent the transformation that inverts the 4,5-axes and leaves the 0, 1, 2, 3-axes unaffected.
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Loewet, M.E. (1981). SO(3,2) for oscillator and hydrogenlike systems. In: Dodonov, V.V., Man'ko, V.I. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54040-7_93
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