91 research outputs found
On the homotopy classification of elliptic operators on stratified manifolds
We find the stable homotopy classification of elliptic operators on
stratified manifolds. Namely, we establish an isomorphism of the set of
elliptic operators modulo stable homotopy and the -homology group of the
singular manifold. As a corollary, we obtain an explicit formula for the
obstruction of Atiyah--Bott type to making interior elliptic operators
Fredholm.Comment: 28 pages; submitted to Izvestiya Ross. Akad. Nau
Wigner phase space distribution as a wave function
We demonstrate that the Wigner function of a pure quantum state is a wave
function in a specially tuned Dirac bra-ket formalism and argue that the Wigner
function is in fact a probability amplitude for the quantum particle to be at a
certain point of the classical phase space. Additionally, we establish that in
the classical limit, the Wigner function transforms into a classical
Koopman-von Neumann wave function rather than into a classical probability
distribution. Since probability amplitude need not be positive, our findings
provide an alternative outlook on the Wigner function's negativity.Comment: 6 pages and 2 figure
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