Moduli of Quanta

The classical phase of the matrix model of 11–dimensional M–theory is complex, infinite–dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex–differentiable structures that can be placed in 1–to–1 correspondence with families of coherent states in the Hilbert space of quantum states. The moduli space of nonbiholomorphic complex structures on classical phase space turns out to be an infinite–dimensional symmetric space. We argue that each choice of a complex differentiable structure gives rise to a physically different notion of an elementary quantum.