Flows on Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras and Time Evolution of Quantum Systems
arXiv:1212.4882
Abstract
In arXiv:1212.2613, we associated a presheaf Σ^A with each unital C*-algebra A. The spectral presheaf Σ^A generalises the Gelfand spectrum of an abelian unital C*-algebra. In the present article, we consider one-parameter groups of automorphisms of the spectral presheaf, in particular those arising from one-parameter groups of inner automorphisms of the algebra. We interpret the spectral presheaf as a (generalised) state space for a quantum system and show how one can use flows on the spectral presheaf and on associated structures to describe the time evolution of non-relativistic quantum systems, both in the Schrödinger picture and the Heisenberg picture.
28 pages, no figures; v2: improved presentation, minor corrections, all main results unchanged
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- Topos quantum theory with short posets