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Ladder operators, a technical question

  1. Nov 12, 2009 #1
    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.
  2. jcsd
  3. Nov 12, 2009 #2


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    Science Advisor

    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.
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