# Individual Particle Localization per Relativistic de Broglie–Bohm

## Abstract

The significance of the de Broglie/Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the (orthodox) single-particle Newton–Wigner position. The effect of non-positive excursions of the ensemble density for extreme cases of positive-energy waves is easily computed using an integral of the equations of motion developed here for free spin-0 particles in 1 + 1 dimensions and is interpreted in terms of virtual-like pair creation and annihilation beneath the Compton wavelength. A Bohm-theoretic description of the acausal explosion of a specific Newton–Wigner-localized state is presented in detail. The presence of virtual pairs found is interpreted as the Bohm picture of the spatial extension beyond single point particles proposed in the 1960s as to why space-like hyperplane dependence of the Newton–Wigner wavefunctions may be needed to achieve Lorentz covariance. For spin-1/2 particles the convective current is speculatively utilized for achieving parity with the spin-0 theory. The spin-0 improper quantum potential is generalized to an improper stress tensor for spin-1/2 particles.

## Keywords

Dirac de Broglie Bohm Relativistic Newton–Wigner Acausal Spin tensor Stress Pair creation Particle## Notes

### Acknowledgement

The author thanks Gordon Fleming for many discussions about Newton–Wigner localization.

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