Is there any Bohmian approach to quantum electrodynamics?

[Ali Lavasani]

I know that in some Bohmian papers (like https://arxiv.org/pdf/quant-ph/0303156.pdf), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the configuration space. My question is, is there any Bohmian approach to reproduce all of the predictions of QED, such as the electromagnetic force created by the exchange of virtual photons, electron self-energy correction, etc?

 

[atyy]

There are old attempts by Bohm and Bell referred to by this more recent attempt.
https://arxiv.org/abs/0707.3487
Also, since Bohmian Mechanics can arguably reproduce non-relativistic quantum mechanics, to the extent the non-relativistic QM can approximately reproduce QED, then Bohmian Mechanics would also approximately reproduce QED.
https://arxiv.org/abs/1503.02312
One should also note other attempts for non-relativistic lattice models (not sure if they can be experimentally realized) whose low energy regime approximates relativistic QED.
https://arxiv.org/abs/hep-th/0507118

 

[A. Neumaier]

One should also note other attempts for non-relativistic lattice models (not sure if they can be experimentally realized) whose low energy regime approximates relativistic QED.https://arxiv.org/abs/hep-th/0507118

This is an inaccurate rendering of what the model in the paper cited does.

As the authors explicitly discuss on p.9, an appropriate low energy approximation produces a Lorentz invariant effective field theory resembling QED in that one has a U(1) gauge boson (representing the photon) and 4 massless fermions (giving too many kinds of electrons, and with the wrong mass).

Moreover (and the authors are silent about this), the effective interaction will have (as always in an effective theory) all possible Lorentz and gauge invariant terms, and not only the minimal coupling that characterized QED. It is not at all clear whether the nonminimal terms are negligible at low energy.

 

[Ali Lavasani]

There are old attempts by Bohm and Bell referred to by this more recent attempt.
https://arxiv.org/abs/0707.3487
Also, since Bohmian Mechanics can arguably reproduce non-relativistic quantum mechanics, to the extent the non-relativistic QM can approximately reproduce QED, then Bohmian Mechanics would also approximately reproduce QED.
https://arxiv.org/abs/1503.02312
One should also note other attempts for non-relativistic lattice models (not sure if they can be experimentally realized) whose low energy regime approximates relativistic QED.
https://arxiv.org/abs/hep-th/0507118

What are the "beables" in such theories that determine the result of an experiment? In BM, the beables are positions of particles which are distributed with the psi-squared. What are these "beables" in these Bohmian approaches to QED? If they are not particle positions, can they be said to be "Bohmian approaches"?

 

[atyy]

What are the "beables" in such theories that determine the result of an experiment? In BM, the beables are positions of particles which are distributed with the psi-squared. What are these "beables" in these Bohmian approaches to QED? If they are not particle positions, can they be said to be "Bohmian approaches"?

They are Bohmian in the broad sense of using a unitarily evolving quantum state to which are added variables to solve the measurement problem.