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

Phase Space Non-commutativity and its Stability