Hamiltonian quantization of complex Chern-Simons theory at level-k

Han M (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Journal of High Energy Physics Springer Verlag (Germany) / Institute of Physics / Scuola Internazionale Superiore di Studi Avanzati (SISSA)

Book Volume: 2025

Article Number: 158

Journal Issue: 12

DOI: 10.1007/JHEP12(2025)158

Abstract

This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group at an even level. Our approach follows the procedure of combinatorial quantization to construct the operator algebras of quantum holonomies on 2-surfaces and develop the representation theory. The *-representation of the operator algebra is carried by the infinite dimensional Hilbert space and closely connects to the infinite-dimensional *-representation of the quantum deformed Lorentz group. The quantum group also emerges from the quantum gauge transformations of the complex Chern-Simons theory. Focusing on a m-holed sphere Σ0,m, the physical Hilbert space is identified by imposing the gauge invariance and the flatness constraint. The states in are the -invariant linear functionals on a dense domain in. Finally, we demonstrate that the physical Hilbert space carries a Fenchel-Nielsen representation, where a set of Wilson loop operators associated with a pants decomposition of Σ0,m are diagonalized.

Involved external institutions

Florida Atlantic University US United States (USA) (US)

How to cite

APA:

Han, M. (2025). Hamiltonian quantization of complex Chern-Simons theory at level-k. Journal of High Energy Physics, 2025(12). https://doi.org/10.1007/JHEP12(2025)158

MLA:

Han, Muxin. "Hamiltonian quantization of complex Chern-Simons theory at level-k." Journal of High Energy Physics 2025.12 (2025).

BibTeX: Download