Remarks on geometric quantum mechanics

Differential geometry of density states

“…This violation of unitarity seems to have an interpretation in terms of quantum measurements and provides a possible useful description of the wave function collapse [17]. We shall develop these considerations elsewhere.…”

Frame functions in finite-dimensional quantum mechanics and its Hamiltonian formulation on complex projective spaces

“…It is introduced just for future convenience. As we shall see shortly, κ affects the form of the classical-like observables associated with the quantum ones (8) and in the litterature κ is usually assumed to be either 1 [BH01] or 1/2 [BSS04]. The symplectic structure allows us to take advantage of the usual Hamiltonian machinery, whose relation with quantum mechanics formalism will be examined shortly.…”

On some hydrodynamical aspects of quantum mechanics

“…VIII). In the fundamental representation, a spin Hamiltonian generates infinitesimal rotations around an axis connecting the two eigenstates (see also Section 4, and [5], [6], for a fairly general geometric picture of Schrödinger's Hamiltonians). A spin wave function ultimately becomes a polynomial χ = χ(ζ) of degree 2s, and can be viewed as a meromorphic function on S 2 (i.e.…”

“…The present note can be viewed as a follow-up of [5] and [6] in that it explores geometric and more generally "classical" features of the standard quantum mechanical formalism, in the hope of shedding some light on delicate conceptual issues, such as entanglement or quantum measurement (see the above references), or, at least, to get an intuitive grip on traditionally elusive topics. So we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil construction of the irreducible unitary representations of SU (2), and looking at the (Madelung-Bohm) velocity attached to the ensuing spin wave functions.…”