fraction

The passage around this formula

The Newton–Wigner operator was not built for elegance; it was built to repair a specific, observable pathology in the naive Dirac position operator $\hat{\mathbf x}$ , the coordinate that appears literally in the Dirac equation. Because a free Dirac wavepacket generically mixes positive- and negative-energy plane-wave components, $\hat{\mathbf x}$ 's Heisenberg equation of motion picks up, alongside the ordinary uniform drift, an oscillating term with no classical counterpart: an angular frequency $\omega_Z = \frac{2Mc^2}{\hbar}$. set purely by the rest mass. For an electron this is $\omega_Z$ $\approx$ 1.55$\times$10^{21}\ $\mathrm{rad\,s^{-1}}$ , an oscillation period of roughly four zeptoseconds in the particle’s…

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