I am still a novice of Maple, but I want to carry out recurvive applications of some formula that involves non-commutative operators X and Y ([X,Y] = XY-YX). I used the following code, but I do not know how to tell Maple a rule that [X,X] = [Y,Y] = 0:

with(Physics);
Setup(mathematicalnotation = true);
Setup(noncommutativeprefix = {X, Y});

Z := X + Y + (1/2)*Commutator(X,Y);
subs(X=Y,Z);

The output is like this:

> Z := X + Y + (1/2)*Commutator(X,Y);
                          Z := X + Y + 1/2 [X, Y][-]

> subs(X=Y,Z);
                              2 Y + 1/2 [Y, Y][-]

The above [Y,Y] must be interpreted as zero, of course.

Thank you very much.