Mixed Translations

by Fedele Lizzi

Wednesday 26 Feb 2025, 16:00 → 17:00 Europe/Rome

2G26

A Lie group is a topological space, in particular a manifold. To each of its points there is associated an element of the group, which is usually represented as a transformation of a vector space. Geometrically points are the pure states of the commutative algebra of the functions on the manifold. Mixed states are instead represented by positive normalised probability densities. We will propose to consider the transformations connected to these mixed states, and find that they form a semigroup. We will then investigate the simple case of one-dimensional translations, and find  interesting surprises, including a novel way to see the connections between temperature and time for thermal states.