Question: AntiCommutator does not work

I am trying to define some AntiCommutator-Relation to work with operators depending on a large number of creation- and annihilation-operators in the fermionic case.

Let "b" be the creation and "a" be the annihilation-operator. Then i am looking, for example, for "a[i]a[j]b[k]a[l]a[m]"...

Now I define the relations:

################

restart

with(Physics)

Setup(quantumop={a,b},algebrarule={%AntiCommutator(a[i],a[j])=KroneckerDelta[i,j],%AntiCommutator(a[i],a[j])=0,%AntiCommutator(b[i],b[j])=0})

################

This works very well for, say, computing the anticommutator of a[m] and a[n]. But this is in the definition, so, no surprise.

But: trying this:

################

AntiCommutator(a[i]a[j],b[k]b[l])

...

expand(%)

################

just does not work. Maple is doing nothing. Just gives the anticommutator back.

And: If i use the %Commutator in case of the %AntiCommutator it works very well and gives exactly the answer i want to have. But not in case of the %AntiCommutator.

 

So, can anyone say what am i doing wrong or has anyone the same problem? thanks

Please Wait...