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SUMMARY:Quantum states as measures on the spectral presheaf - Andreas Dör
 ing\, Oxford University
DTSTART:20091117T141500Z
DTEND:20091117T154500Z
UID:TALK20779@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:States of a physical system -- classical or quantum -- can be 
 seen as normed positive linear functionals (i.e.\,\nintegrals) on the alge
 bra of physical quantities. In classical physics\, where the algebra is ab
 elian\, states areequivalently described by measures on the state space. A
  quantum system has a nonabelian algebra of\nphysical quantities\, and the
 re is no obvious notion of a state space. We will show how quantum states 
 can also\nbe understood as measures\, but now defined on a certain preshea
 f\, called the spectral presheaf\, which takes\nthe role of the state spac
 e of the quantum system. The spectral presheaf is a central object in the 
 topos\napproach to quantum theory. It will be shown how the spectral presh
 eaf is related to\, but different from the\nGel'fand spectrum of a certain
  topos-internal operator algebra.
LOCATION:MR9\, Centre for Mathematical Sciences
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