The well-known commutation relations for the p and q operators follow directly from the differentiation rules.

The commutation relations, in addition to those of the Poincaré group, are as follows:

By the use of the commutation relations the second line follows from the first.

From the commutation relations the possible eigenvalues can be found.

Terms were added to the commutation relations to cancel out the delta term in Eq.

Notice that since (by the commutation relations) the order in which we write the annihilation operators does not matter.

This looks very similar to the commutation relation of the position and momentum operator.

The components have the following commutation relations with each other:

This can be derived starting from the commutation relations in the previous section.

The commutation relations are simply carried over to infinite dimensions .