Article 08264 introduces the spin group, a special double cover of the group of Lorentz transformations that may be expressed as compositions of even numbers of reflections. This article introduces the Dirac equation in flat spacetime. This is a differential equation whose group of symmetries automatically includes the spin group. This article explores the pattern of symmetries of the Dirac equation in d-dimensional flat spacetime, including antlinear symmetries like CPT symmetry. The definition of symmetry used here is motivated by quantum field theory, where the Dirac equation occurs as the equation of motion for a free spinor field. This article also explores symmetries of the Weyl equation, which is defined only when d is even. This is another differential equation whose group of symmetries automatically includes the spin group.
