Answer to Question #166382 in Mechanics | Relativity for Rajeev Sharma

Question

Explain Lorentz invariance of Dirac equation . Deduce the condition for the invariance

Answer 1

Consider two inertial frames, $S$ and $S'$ . Let the $x^\mu$ and $x^{\mu^{'}}$be the space-time coordinates of a given event in each frame, respectively. These coordinates are related via a Lorentz transformation, which takes the general form;

$x^{{\mu}^{'}}=a^{\mu}_{v}x^y$ , where the $a^{{\mu}{'}}$ are real numerical coefficients that are independent of the $x^{\mu}$

In frame $S$, the Dirac equation is written as;

$[\gamma^\mu(P_\mu-\frac{e}{c}\Phi_\mu)-m_ec]\psi=0$