>>14154767If you need it explicitly spelled out for you, by "commutator" you can think "Lie derivative" or in other words, [A,B] is the infinitesimal change in B as you move A.
This should make things very physically clear. When the bracket is just the Poisson bracket as in classical mechanics, the above definition makes it clear that [A,B] gives you the infinitesimal change in whatever quantity B you're looking at when you vary A, so
which should be very familiar from Hamiltonian stuff.
In fact, if these were coordinates, the bracket would literally the directional derivative.
Quantum mechanically, it's the exact same thing, except the bracket is the commutator.
>>14154775>you are not readingsomeone certainly isn't
you still cannot even explain your issue
>>14154781the identity of a vector space is the 0 element.
vectors act as derivatives on functions, and that does have a multiplicative identity - all you are doing is confusing operations
