The Pin Groups in Physics: C, P, and T

  title={The Pin Groups in Physics: C, P, and T},
  author={Marcus Berg and Cecile DeWitt-Morette and Shangjr Gwo and Erik Kramer},
  journal={arXiv: Mathematical Physics},
We review the role in physics of the Pin groups, double covers of the full Lorentz group. Pin(1,3) is to O(1,3) what Spin(1,3) is to SO(1,3). The existence of two Pin groups offers a classification of fermions based on their properties under space or time reversal finer than the classification based on their properties under orientation preserving Lorentz transformations -- provided one can design experiments that distinguish the two types of fermions. Many promising experimental setups give… 

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