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Hermitian vector - dma unifi

Hermitian vector - dma unifi 2025

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The document discusses the analysis of Hermitian vector fields and special phase functions within the context of both Galilei and Einstein spacetimes. It begins by exploring the Lie algebra of Hermitian vector fields associated with a Hermitian line bundle, followed by a detailed examination of the geometric structures in both frameworks. The authors establish a correspondence between Hermitian vector fields and special phase functions, highlighting their isomorphism in both cases. The paper also compares classical and quantum mechanics formulations in these two spacetimes, emphasizing differences in metric structures, phase spaces, observer roles, and the treatment of gravitational and electromagnetic fields. Ultimately, it presents a unified approach to understanding quantum operators through the classification of Hermitian vector fields.

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