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I've been reading some beginner books about quantum electrodynamics / quantum field theory (e.g. Feynman's QED book), and basically everything is done at the paper and pencil level.

I'm curious if there is QED (or QFT) software, similar to the many quantum chemistry software packages out there. In particular: what software would one use to calculate the absorption spectrum of a really simple system, like the hydrogen or helium atom, at the QED level?

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  • $\begingroup$ If you're talking about calculating QED-induced corrections to the Schrodinger equation, like the Lamb shift, then all you need is a numerical integration package. If instead you're talking about calculating QED bound states from first principles...then that's a whole other beast. Bound states in QCD have been calculated using lattice QFT, I've never heard of anything similar with QED. $\endgroup$
    – AfterShave
    Commented Sep 18, 2023 at 7:54
  • $\begingroup$ @AfterShave Welcome to our new community! Thanks for your contribution, and we hope to see much more of you in the future! For this type of question, usually the asker is looking for more than just a numerical integration package with which s/he can type in the integrands themselves. Ideally there would be a software package that already has the integrands coded (no matter how "trivial" that may be), for example the paper cited at the end of my answer describes a software that completely does certain QED corrections for the user. $\endgroup$ Commented Sep 18, 2023 at 14:59
  • $\begingroup$ @AfterShave I was indeed thinking of something closer to "calculating QED bound states from first principles". I'd be quite interested in the lattice QFT treatment as well, please do post an answer about that. $\endgroup$
    – Alex I
    Commented Sep 18, 2023 at 15:39
  • $\begingroup$ @AlexI From what I have seen, bound state energies are extremely accurate when solving the non-relativistic Schroedinger, even more accurate after adding corrections to account for special relativity (e.g. with the X2C Hamiltonian), and QED corrections (self-interaction, vacuum polarization, recoil, etc.) provide extremely minor corrections (not something that will be obvious in an absorption spectrum like you requested in your question, but more like something that changes the final digits in the energy). [Continued in next comment...] $\endgroup$ Commented Sep 18, 2023 at 16:23
  • $\begingroup$ I don't know of software that calculates energy levels of arbitrary atoms "from first principles QED", and it's apparently extremely hard when you have more than 1 electron. $\endgroup$ Commented Sep 18, 2023 at 16:24

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GRASP

Allow me to introduce you to GRASP, a software that was written largely by now 92-year-old Ian Grant and now 94-year old (5 days from now) Charlotte Froese Fischer whose PhD supervisor was Douglas Hartree from the Hartree-Fock method; but the software has been maintained throughout all of these decades and is open source on GitHub with some commits to "GRASP 2018" being pushed within the last year!

GRASP stands for General Relativistic Atomic Structure Program and was originally written in an older version of FORTRAN, but it has been modernized to Fortran 90 and is parallelized using MPI. In addition to the first link that I provided, which is the HTML/doxygen (web-based) version of the documentation, the the PDF version is available here.

QED effects:

If you click on the first link and search QED in the search bar, you'll see a variety of QED functions and other results, which I'll list below:

qed
qed.f90
qed_i
qed_I.f90
qed_slfen
qed_slfen.f90
qed_slfen_i
qed_slfen_I.f90
qedcut_c
qedcut_C.f90

Also if you search QED in the PDF documentation which I linked earlier in this answer, you'll find that the vacuum polarization and self-energy terms, which are considered the leading QED effects are included in the rci (relativistic CI) routine:

rci,            rci_mpi - perform relativistic configuration interaction (RCI) calculation with transverse photon (Breit) interaction and vacuum polarization and self-energy (QED) corrections.

Although the term QED appears 30 more times in that document, it's all in relation to the RCI routine, and there's a reference from over 40 years ago by Ian Grant himself (and others) in relation to QED corrections for the multi-configurational Dirac-Fock (MCDF) method, which can be considered a relativistic version of MCSCF (see What are the types of MCSCF?):

B.J.McKenzie, I.P.Grant and P.H.Norrington "A program to calculate transverse Breit and QED corrections to energy levels in a MCDF environment" Computer Physics Communications. 21, 233-246 (1980); ibid 23, 222 (1980).

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