The Dirac equation is a relativistic wave equation unifying special relativity and quantum mechanics, whose structure is built from an imaginary-unit term, gamma matrices, a four-gradient, mass and speed-of-light terms, and a spinor wave function. Lorentz invariance is achieved because the gamma matrices (contravariant) and the four-gradient (covariant) contract together to form a scalar quantity, which by definition does not change under Lorentz transformation. This places the equation within relativistic quantum mechanics, where scalar invariants under coordinate transformation are the mechanism by which a physical law is guaranteed to hold in every reference frame.
The Dirac equation is a relativistic wave equation unifying special relativity and quantum mechanics, whose structure is built from an imaginary-unit term, gamma matrices, a four-gradient, mass and s…