Date: 2024-03-07 | Article ID: 21794 |

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.

**2024-03-07**(added a reference to a review of antilinear operators)**2023-06-02**(replaced some references with cross-references to a new article)**2023-05-28**(first version)

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