Every finite-dimensional GKLS dissipator is the contraction of a universal trilinear map D(X,Y)Z=XZY−½{YX,Z} whose components depend only on the Lie-Jordan structure tensors B and C.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
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abstract
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
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A Lie-Jordan Geometric Formulation of Lindblad Dynamics
Every finite-dimensional GKLS dissipator is the contraction of a universal trilinear map D(X,Y)Z=XZY−½{YX,Z} whose components depend only on the Lie-Jordan structure tensors B and C.