Example for proton

[alexchandel]

Could you post a self-contained example for computing proton values? Obviously not one with useful accuracy (or reasonable execution time); just an example that is correct in form and would approach accuracy in the limit of infinite resources.

[mspraggs]

Hi @alexchandel 👋🏻

Unfortunately I'm not familiar with the calculations required to calculate baryonic observables on the lattice. The collaboration I worked in focussed mainly on mesonic quantities. (I left academia in 2016, so I can barely remember the mesonic bits 😅)

pyQCD should let you compute quark propagators for a given gauge field using the Wilson fermion action. These propagators can then be used to compute baryonic interpolators and correlation functions. Depending on the quantum numbers of the baryon, you will need to contract the propagators in a particular way. This is covered in Gattringer and Lang in chapter 6. I'm afraid I no longer have the detailed knowledge required to assist you beyond this though 😞

I hope you find the answers you seek!

[alexchandel]

Thank you for the response. Do you have any pyQCD meson examples from your work? The examples directory is a little sparse, so anything you have would be helpful.

[mspraggs]

Now you're really asking 😄

Because it can only run on a single machine, this package was never up to computing anything physically meaningful, so I didn't really develop that functionality, at least not in the current version of the package. (This was more of a hobby project to learn how the calculations work under the hood.)

That said, digging through some old code, I've turned this up. It takes quark propagators and uses the Numpy einsum function to contract (I think that's the right term, it's been so long 😄) those propagators with two gamma matrices.

You could add this on top of the example here. The LatticeColourVector and LatticeColourMatrix types should support the Cython buffer protocol, which I think should allow you to pass them directly to the einsum function, but YMMV. Worst case you can convert them to a Numpy ndarray and use that instead.