Nonassociative structure of quantum mechanics in curved space-time Conventional approach to quantum mechanics in phase space, ͑q , p͒, is to take the operator based quantum mechanics of Schrödinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q-or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
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