1212.4882 (Andreas Doering)

Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras II: Flows
and Time Evolution of Quantum Systems    [PDF]

Andreas Doering

In arXiv:1212.2613, we associated a presheaf \Sigma^A with each unital C*-algebra A. The spectral presheaf \Sigma^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, arising for example 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 we can use flows on the spectral presheaf and on associated structures to describe the time evolution of non-relativistic quantum systems, both in the Schr\"odinger picture and the Heisenberg picture.

View original: http://arxiv.org/abs/1212.4882