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Title:
From Quantum Mechanics to Symplectic Topology and Back
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Abstract:
Algebras of functions of certain symplectic manifolds admit quasi-states, a class of functionals which are linear on all Poisson-commutative subalgebras but not on the whole algebra. Their origins go back to foundations of quantum mechanics, while their construction involves methods of Floer theory. It turns out that quasi-states enable one to detect footprints of symplectic rigidity in quantum mechanics.
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