Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

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dc.creatorOrtega, Ramon
dc.creatorSantander, Mariano
dc.date2001-12-14
dc.date.accessioned2026-07-07T10:54:13Z
dc.date.available2026-07-07T10:54:13Z
dc.descriptionThis paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.
dc.description46 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math-ph/0112030
dc.identifierhttp://arxiv.org/abs/math-ph/0112030
dc.identifierJ.Phys.A35:7877-7918,2002
dc.identifierdoi:10.1088/0305-4470/35/37/303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185734
dc.subjectMathematical Physics
dc.titleTrigonometry of 'complex Hermitian' type homogeneous symmetric spaces
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