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arXiv · 1608.05340

Relativistic Kinematics of Two-Parametric Riemann Surface in Genus Two

A. V. Nazarenko·Yu. A. Kulinich
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Abstract

It is considered a model of compact Riemann surface in genus two, represented geometrically by two-parametric hyperbolic octagon with an order four automorphism and described algebraically by the corresponding Fuchsian group. Introducing the Fenchel--Nielsen variables, we compute the Weil--Petersson (WP) symplectic two-form for parameter space and analyze the closed isoperimetric orbits of octagons. WP-Area in parameter space and the canonical action--angle variables for the orbits are found. Exploiting the ideas from the loop quantum gravity, we generate relativistic kinematics by the Lorentz boost and quantize WP-area. We treat the evolution in terms of global variables within the "big bounce" concept.

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A. V. Nazarenko, Yu. A. Kulinich. 2016-08-18. Relativistic Kinematics of Two-Parametric Riemann Surface in Genus Two. https://arxiv.org/abs/1608.05340

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