Re: Commutators with boson operators

*To*: mathgroup at smc.vnet.net*Subject*: [mg97875] Re: Commutators with boson operators*From*: Simon <simonjtyler at gmail.com>*Date*: Tue, 24 Mar 2009 05:32:55 -0500 (EST)*References*: <200903211016.FAA14634@smc.vnet.net> <gq557g$87v$1@smc.vnet.net>

On Mar 22, 7:51 pm, Filippo Miatto <mia... at gmail.com> wrote: > For the creation and annihilation operators you could use their matrix = > form, you can find it in The Quantum Theory of Fields Vol. 1 by Weinberg > > On Mar 21, 2009, at 11:16 AM, Volodymyr wrote: > > > Hello, > > I need some help. > > > I want to write code that Mathematica would calculate commutators > > [A,B], [A,[B,C]] and so on..., > > > where A,B,C,D,... are functions like > > > A = a+ b*creat + c*annih + d*creat**annih + e*annih**creat + > > f*creat^2+g*annih^2+... > > > where a,b,c,d,... are usual complex numbers; > > > and annih & creat are boson noncommutative operators > > that satisfy commutation relation: > > [annih, creat] = 1. > > > Thank you in advance! You could define a function com[a_,b_] and make it bilinear and satisfy the Jacobi identity and make it a derivation, [a,bc]=[a,b]c+b[a,c], so that it recursively reduces any expression down to the basic commutators [a,a]=0=[a^\dag,a^\dag] , [a^\dag,a]=1. Simon

**References**:**Commutators with boson operators***From:*Volodymyr <ktpist@ukr.net>