nLab Alejandro Uribe

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Selected writings

On quantization of Chern-Simons theory in terms of Weyl quantization and skein relations:

• Răzvan Gelca, Alejandro Uribe: The Weyl quantization and the quantum group quantization of the moduli space of flat $SU(2)$-connections on the torus are the same, Commun. Math. Phys. 233 (2003) 493-512 [arXiv:math-ph/0201059]

• Răzvan Gelca, Alejandro Uribe: Quantum mechanics and non-abelian theta functions for the gauge group $SU(2)$ [arXiv:1007.2010]

On the integer Heisenberg group describing the phase space of abelian Chern-Simons theory on closed Riemann surfaces (and its relation to skein relations and theta functions):

• Răzvan Gelca, Alejandro Uribe: From classical theta functions to topological quantum field theory, in: The Influence of Solomon Lefschetz in Geometry and Topology: 50 Years of Mathematics at CINVESTAV, Contemporary Mathematics 621, AMS (2014) 35-68 [arXiv:1006.3252, doi;10.1090/conm/621, ams:conm-621, slides pdf, pdf]

Related entries

• theta function

• quantization of 3d Chern-Simons theory

• Stone-von Neumann theorem

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