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A fully relativistic (Lorentz covariant) description, first put forward by Paul Dirac in 1928, of the first quantized, spin one half fermion with nonzero mass. Physical notions to do with this equation include the Dirac sea, Dirac hole theory, the Klein Paradox and the fine structure of the Hydrogen spectrum.
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Wave function - Dirac Notation
The equation above makes use of the Einstein's summation convention. According to this convention, all the repeated indices get summed over.
Eq: $$x^\mu y_\mu \equiv \sum_{\mu=0} x^0y_0 + x^1y_1 + .. …