Geometrical description of algebraic structures: Applications to Quantum Mechanics

Alberto Ibort; Giuseppe Marmo; Giuseppe Morandi; Jos\'e F. Cari\~nena

Geometrical description of algebraic structures: Applications to Quantum Mechanics

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arxiv 1209.4583 v1 pith:S7IBJ5Y4 submitted 2012-09-20 math-ph math.MP

Geometrical description of algebraic structures: Applications to Quantum Mechanics

Jos\'e F. Cari\~nena , Alberto Ibort , Giuseppe Marmo , Giuseppe Morandi This is my paper

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keywords mechanicsquantumtheoriesalgebraicgeometricalgeometrizationphysicalstructures

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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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Cited by 1 Pith paper

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A Lie-Jordan Geometric Formulation of Lindblad Dynamics
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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.