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Hope all is well. I am trying to understand the process that takes us from the Pauli equation to the Dirac equation. Whilst I understand the motivation is to have a lorrentz covariant equation I don't really understand A.) how this was done B.) what the physical result is of the new covariant equation, what new info are we getting?.

Lorrentz covariance is a fairly new concept to me so just trying to get a proper sense of what it physically means. Any and all enlightenent is much appreciated :) cheers