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For learning something about the degrees of freedom and underlying path integral math, is it possible to do some kind of scalar QED or normal QED simulation on a lattice in the same way Lattice QCD is done? Mainly to get a better grip on how the fields couple together and how the vacuum behaves etc, in a way that is not dependent on perturbation theory and Feynman diagrams at all.

Lattice QCD is very simple to express (though it is very computationally heavy to extract some kind of verifiable quantitative results), I was hoping there would be some way to do something analogous with QED or scalar QED. Maybe calculating some very simple interactions, maybe with a "quenched" electron (fixed) and just doing some photon field interactions. I've tried searching for this and have come up shorthanded (I guess because the perturbative QED approach is so successful at predicting observables that can be tested in accelerators).

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  • $\begingroup$ QED and QCD are both Yang-Mills gauge theories and as such can both be simulated by similar application of lattice Yang-Mills just for different groups and representations. QED is just too simple to be worth it in most cases. $\endgroup$
    – Gabriel Golfetti
    Commented Jan 8, 2023 at 20:46
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    $\begingroup$ @GabrielGolfetti yeah I assumed as much, but would be helpful if there was any kind of code or literature on the subject - like I wrote, it's mainly for learning (I do have a bunch of intros to Lattice QCD already) $\endgroup$
    – BjornW
    Commented Jan 8, 2023 at 20:57
  • $\begingroup$ I don’t know much about lattice gauge theory, but I wonder whether you could use it to calculate the lifetime of positronium. $\endgroup$
    – Ghoster
    Commented Jan 9, 2023 at 1:26
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    $\begingroup$ This paper might be of interest. $\endgroup$
    – Ghoster
    Commented Jan 9, 2023 at 1:38
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    $\begingroup$ It is always instructive when learning computational methods to start with problems where the analytical answer is known, so you get a feeling for how well the methods work and possible problems. Does "shorthanded" mean you are looking for something other than the thousand papers returned for "lattice QED" (in quotes) by Google Scholar? If by "doing something instructive" you mean QED problems that can't be easily solved perturbatively, then you might look at non-perturbative problems such as those involving monopoles, super heavy nuclei with Z>137, intense laser fields, …. $\endgroup$
    – David Bailey
    Commented Jan 10, 2023 at 16:40

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