Connecting to Physics
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The parity violation of Dirac spinor fields occurs to the level of the Pauli (or Weyl) subspinor fields. So in physics the fundamental fermion fields are Pauli spinors instead of Dirac spinors. Dirac spinors consist of a pair of Pauli spinors; the Dirac algebra is the Pauli algebra tensored with R(2). This extra R(2) is required not only of this physical context, but also of mathematical contexts, like using O L (2) to represent R 8,0 and triality operations (see chapter 7), and in the construction of the groups of the magic square (see chapter 8). This paradigm, that the Clifford algebra of spacetime starts with a Pauli algebra for just space, and that this when tensored with R(2) provides room for time, will also be used below in the construction of a Clifford algebra for (1,9)-spacetime.
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