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Feb 16, 2009 - May 4, 2017 - Feb 3, 2014 - Relativistic Quantum. Mechanics. 1. 1.1 Special Relativity. 1. 1.2 One-particle states. 7. 1.3 The Klein–Gordon equation. 9. 1.4 The Dirac equation. 14. 1.5 Gauge in field theory by considering fields which themselves transform non-trivially under the. Lorentz group. In this section we will describe the Dirac equation, whose Dirac equation. However, we do not know yet how to transform the 4-dimensional wave function. ? and the Dirac matrices ?µ. Lorentz Transformation of The Lorentz transformation generators are 4 ? 4 matrices as follows: Jk. = ( 1. 2 ?k. 0 Exercise. Let U be a Dirac spinor and suppose that U obeys the equation. Feb 6, 2018 - Attempts to blend quantum mechanics and special relativity led to the problem of infinities. 1 The “plane wave solution” of the Dirac equation ?(x) = u(p)e. ?ipx.Similarly, Dirac equation is Lorentz covariant, but the wavefunction will change when we make a Lorentz transformation. Consider a frame F with an observer O.