Wednesday 7 October 2020

special relativity - Why in the relativistic quantum mechanics $ gamma_4$ name is not used instead of $ gamma_5$?


I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why the name of the new matrix has not been given as $$\gamma_4.$$ Is there any historical reason behind this or it is simply taken as $$\gamma_5$$ without any special reason skipping $$\gamma_4~?$$



Answer



From Wikipedia:



The number 5 is a relic of old notation in which $\gamma^0$ was called "$\gamma^4$".




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