Quantum states as measures on the spectral presheaf
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If you have a question about this talk, please contact Julia Goedecke.
States of a physical system—classical or quantum—can be seen as normed positive linear functionals (i.e.,
integrals) on the algebra of physical quantities. In classical physics, where the algebra is abelian, states areequivalently described by measures on the state space. A quantum system has a nonabelian algebra of
physical quantities, and there is no obvious notion of a state space. We will show how quantum states can also
be understood as measures, but now defined on a certain presheaf, called the spectral presheaf, which takes
the role of the state space of the quantum system. The spectral presheaf is a central object in the topos
approach to quantum theory. It will be shown how the spectral presheaf is related to, but different from the
Gel’fand spectrum of a certain toposinternal operator algebra.
This talk is part of the Category Theory Seminar series.
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