Ladder operators, a technical question

[actachyon]

Forgive me if I am putting this in the wrong place, but this is my first post here. The question that I have is directed to the more experienced researchers than I am, I guess.

In the Hamiltonian formulation of QFTs we write everything in terms of the ladder operators, right? So in practice that means that we have to deal with commuting of long sequences of the ladder operators such that they destroy the vacuum bra and in the process pick up terms that have delta functions with momentum variables. This becomes non trivial even for a string of 8, 10 ladder operators. It could be done by hand but at the expense of time. The obvious way to deal with this is to write code! Is anybody aware of such code in either Fortran, C or any other language? I must not be the first one to think of it, it must have been done before. At least, where would be a good place to start looking for this? What are good site that have Fortran libraries devoted to QFT or physics in general?

Thanks in advance.

 

[strangerep]

In the Hamiltonian formulation of QFTs we write everything in terms of the ladder operators, right? So in practice that means that we have to deal with commuting of long sequences of the ladder operators such that they destroy the vacuum bra and in the process pick up terms that have delta functions with momentum variables. [...] The obvious way to deal with this is to write code! [...]

Since this is essentially just repeated manipulations/substitutions based on the commutators
of the Heisenberg algebra, it should be possible to do it using Cadabra.
See http://cadabra.phi-sci.com/

The example workbooks there have some info about how to work with commutators.
(See the one on the Poincare algebra.) You'd have to write some "@substitute" patterns
and use Cadabra's "!" apply-until-nothing-changes-anymore feature.

Realistically, you'd have to invest time reading the manual, and maybe talk
to Cadabra's author to get more help.

 

[Entropia]

Hello,

Thank you for your question. Yes, ladder operators play a crucial role in the Hamiltonian formulation of quantum field theories (QFTs). They are used to create and annihilate particles in a given quantum state and are essential for calculating physical quantities such as energy and momentum.

I understand your concern about the time-consuming process of commuting long sequences of ladder operators. This is a common challenge in QFT calculations. Fortunately, there are several tools and software available to assist in these calculations.

One option is to use computer algebra systems such as Mathematica or Maple, which have built-in functions for manipulating ladder operators. These programs allow for automated calculations of commutation relations and can handle large sequences of operators.

Another option is to use pre-existing codes and libraries specifically designed for QFT calculations. These can be found on various websites and online repositories, such as GitHub. Some popular codes include FeynCalc and FORM, which offer efficient ways to handle ladder operators and perform QFT calculations.

I suggest starting by searching for Fortran or C libraries for QFT on websites such as arXiv, INSPIRE, or the American Physical Society (APS) Physics website. You can also reach out to colleagues or professors who may have experience with QFT calculations and ask for their recommendations.

I hope this helps. Best of luck with your research!