On the relation between geometrical quantum mechanics and information geometry
On the relation between geometrical quantum mechanics and information geometry
Let $(M,g)$ be a compact, connected and oriented Riemannian manifold with volume form $d$ ${vol}_g$. We denoteby $\mathcal{D}$ the space of smooth probability density functions on $M\,,$ i.e.$\mathcal{D}:= \{\rho\in C^{\infty}(M,\mathbb{R})| \rho>0\,\,$and$\,\,\int_{M}\rho\cdot $d${vol}_{g}=1\}\,.$ We regard $\mathcal{D}$ as an infinite dimensionalmanifold. In this paper, we consider the almost Hermitian structure on $T\mathcal{D}$ …