How are the positions of particles described in QFT?

[Hans de Vries]

Localization of relativistic particles in strong attractive potentials may lead to some peculiar (though not necessarily unphysical) effects. For example, imagine an atomic nucleus with charge Z and corresponding attractive Coulomb potential for electrons. The lowest state available for electrons has energy E. If you increase the nuclear charge, the energy E would increase, and at some point (I think this happens at Z > 137) this energy becomes larger than the energy $2mc^2$ required to create one electron-positron pair. As far as I know, such conditions have not been achieved experimentally. However, the current understanding about what happens next is this: The electron-positron pair, indeed, gets created. The electron gets attached to the nucleus, thus effectively reducing its charge to Z-1, and the positron is repelled to infinity.

Note that such pair creation requires a strong external potential. However, if are you simply localizing a free particle in empty space, then there is no reason to expect creation of pairs.

Eugene.

Not surprisingly, The average radius of the electron's orbit at Z=137 becomes
the Compton radius. Compressing a wavefunction into a space smaller as the
Compton radius requires an energy (from external fields or scattering momentum)
which is larger as the rest mass energy and therefor leads to particle production.


Regards, Hans