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Lie Groups, Physics, and Geometry by Robert Gilmore

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7

EXPonentiation

 

 

Linearization of a Lie group to form a Lie algebra introduces an enormous simplification in the study of Lie groups. The inverse process, reconstructing the Lie group from the Lie algebra, is carried out by the EXPonential map. We return to a more thorough study of the exponential map in this chapter. In particular, we address the three problems raised in Chapter 4.   Does the EXPonential operation map the Lie algebra back onto the Lie group? Are Lie groups with isomorphic Lie algebras themselves isomorphic? Are there natural ways to parameterize Lie groups? We close this chapter with a spectrum of applications of the EXPonential mapping in physics. Applications include computing the dynamical evolution of quantum systems ...

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