We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of simple examples and show that a system can be stabilised by introducing quartic interactions provided they satisfy phase-space copositivity. In order to conduct perturbative analysis of these systems one can use either canonical methods or phase-space path integral methods which we present in some detail.
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