Associativity problem with observables

[zetafunction]

let be A , B and C three non-commuting observables

my question is how can one solve the problem with associative property ? i mean

$$(AxB)xC$$ will in general be different from $$Ax(BxC)$$

and if we had 4 A, B ,C ,D instead of three the problem is even worse , how can anyone deal with it ?? i mean since the observable do not commute and we can not apply the associative property is there any ambiguity in QM ?? or similar ??

 

[xepma]

Non-commutativity does not imply non-associativity, so I do not really see your problem here... (for example a non-Abelian group is still associative; the same goes for matrices).