# Creation annihilation operators - expanding brackets

1. Sep 10, 2012

### yaj

I would like to normal order the following product of creation-annihilation operators, set up in Maple 16 as follows. The problem is, Maple won't perform "expand" (lowercase e) on the last step below (evaluating sigma3(x) :=[op1+op2]*[op3+op4]*[op5+op6] ); , which makes setting up the entire previous operator groups useless. Appreciate any help.
Thanks
yaj

> with(Physics);
> Setup(mathematicalnotation = true);
print(output redirected...); # input placeholder
[mathematicalnotation = true]
> am1 := Annihilation(p, 1, notation = explicit);
print(output redirected...); # input placeholder
am1 := a-[p[1]]
> ap1 := Creation(p, 1, notation = explicit);
print(output redirected...); # input placeholder
ap1 := a+[p[1]]
> op1 := am1*exp(-i*p[1]*x);
print(output redirected...); # input placeholder
op1 := a-[p[1]] exp(-i p[1] x)
> op2 := ap1*exp(i*p[1]*x);
print(output redirected...); # input placeholder
op2 := a+[p[1]] exp(i p[1] x)
> am2 := Annihilation(p, 2, notation = explicit);
print(output redirected...); # input placeholder
am2 := a-[p[2]]
> ap2 := Creation(p, 2, notation = explicit);
print(output redirected...); # input placeholder
ap2 := a+[p[2]]
> op3 := am2*exp(-i*p[2]*x);
print(output redirected...); # input placeholder
op3 := a-[p[2]] exp(-i p[2] x)
> op4 := ap2*exp(i*p[2]*x);
print(output redirected...); # input placeholder
op4 := a+[p[2]] exp(i p[2] x)
> am3 := Annihilation(p, 3, notation = explicit);
print(output redirected...); # input placeholder
am3 := a-[p[3]]
> ap3 := Creation(p, 3, notation = explicit);
print(output redirected...); # input placeholder
ap3 := a+[p[3]]
> op5 := am3*exp(-i*p[3]*x);
print(output redirected...); # input placeholder
op5 := a-[p[3]] exp(-i p[3] x)
> op6 := ap3*exp(i*p[3]*x);
print(output redirected...); # input placeholder
op6 := a+[p[3]] exp(i p[3] x)

> sigma3(x) :=[op1+op2]*[op3+op4]*[op5+op6];
print(output redirected...); # input placeholder
sigma3 := Physics:-*(

[a-[p[1]] exp(-i p[1] x) + a+[p[1]] exp(i p[1] x)],

[a-[p[2]] exp(-i p[2] x) + a+[p[2]] exp(i p[2] x)],

[a-[p[3]] exp(-i p[3] x) + a+[p[3]] exp(i p[3] x)])