The space of density states in geometrical quantum mechanics

Details The space of density states in geometrical quantum mechanics The space of density states in geometrical quantum mechanics

2007-07-25

arxiv.org/abs/0707.3759v1

Chapter in the book "Differential Geometric Methods in Mechanics and Field Theory", Volume in Honour of Willy Sarlet, Eds. F.

Physics

Quantum Physics

Amslatex, 18 pages, 4 figures

Scientific paper

We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density states $\D(\Hil)$ from a geometrical perspective identifying the stratification associated to the natural $GL(\Hil)$--action on $\D(\Hil)$ and some of its properties. We apply this construction to the cases of quantum systems of two and three levels.

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