Noncommutativity from spectral flow

We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of spectral flow. Gaps in the energy or mass spectrum may become large which effectively truncates the available state space. Using both operator and path integral languages we explicitly discuss examples in quantum mechanics, (light-front) quantum field theory and string theory.