And in fact some clear signs of this were already present in studies of so-called quantum chaos in the 1980s—although most of the specific cases actually considered involved time-independent constraint satisfaction, not explicit time evolution.

And these amplitudes a i are assumed to be complex numbers with a continuous range of possible values, subject only to the conventional constraint of unit total probability Sum[Abs[a i ] 2 , {i, 2 n }]  1 . … It was found to be sufficient to do operations on just one and two spins at a time, and in fact it was shown that any 2 n × 2 n unitary matrix can be approximated arbitrarily closely by a suitable sequence of for example underlying 2-spin {x, y}  {x, Mod[x + y, 2]} operations (assuming values 0 and 1), together with 1-spin arbitrary phase change operations.

So this led in the 1960s to attempts to base theories just on setting up simple mathematical constraints on the overall so-called S matrix defining the mapping from incoming to outgoing quantum states. … (The Schrödinger equation is like a diffusion equation in imaginary time, so the path integral for it can be thought of as like an enumeration of random walks. … And indeed a recurring issue in it has been difficulty with constraints and redundant degrees of freedom—such as those associated with extended objects.