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CATEGORIES:Category Theory Seminar
SUMMARY:Quantum states as measures on the spectral preshea
f - Andreas DÃ¶ring\, Oxford University
DTSTART;TZID=Europe/London:20091117T141500
DTEND;TZID=Europe/London:20091117T154500
UID:TALK20779AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/20779
DESCRIPTION:States of a physical system -- classical or quantu
m -- can be seen as normed positive linear functio
nals (i.e.\,\nintegrals) on the algebra of physica
l quantities. In classical physics\, where the alg
ebra is abelian\, states areequivalently described
by measures on the state space. A quantum system
has a nonabelian algebra of\nphysical quantities\,
and there is no obvious notion of a state space.
We will show how quantum states can also\nbe under
stood as measures\, but now defined on a certain p
resheaf\, called the spectral presheaf\, which tak
es\nthe role of the state space of the quantum sys
tem. The spectral presheaf is a central object in
the topos\napproach to quantum theory. It will be
shown how the spectral presheaf is related to\, bu
t different from the\nGel'fand spectrum of a certa
in topos-internal operator algebra.
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Julia Goedecke
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