Relativity of $\hbar$

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dc.creatorIsidro, J. M.
dc.date2002-04-22
dc.date.accessioned2026-07-07T04:13:24Z
dc.date.available2026-07-07T04:13:24Z
dc.descriptionLooking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of locally-defined coherent states is the existence of an almost complex structure on ${\cal C}$. A necessary and sufficient condition for globally-defined coherent states is a complex structure on ${\cal C}$. The picture of quantum mechanics that emerges is conceptually close to that of a geometric manifold covered by local coordinate charts. Instead of the latter, quantum mechanics has local coherent states. A change of coordinates on ${\cal C}$ may or may not be holomorphic. Correspondingly, a transformation between quantum-mechanical states may or may not preserve coherence. Those that do not preserve coherence are duality transformations. A duality appears as the possibility of giving two or more, apparently different, descriptions of the same quantum-mechanical phenomenon. Coherence becomes a local property on classical phase space. Observers on ${\cal C}$ not connected by means of a holomorphic change of coordinates need not, and in general will not, agree on what is a semiclassical effect vs. what is a strong quantum effect
dc.description18 pages. LaTeX
dc.identifierhttps://arxiv.org/abs/hep-th/0204178
dc.identifierhttp://arxiv.org/abs/hep-th/0204178
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/51248
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleRelativity of $\hbar$
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