A simple realization of gl(2,c) Lie algebra with vector operators on sphere
Q. H. Liu, X. P. Rong, and D. M. Xun
TL;DR
This paper presents a straightforward method to realize the gl(2,c) Lie algebra on a sphere using basic vector operators, enabling the construction of coherent states based on this algebra.
Contribution
It introduces a simple realization of gl(2,c) Lie algebra on a sphere using elementary vector operators, facilitating the construction of coherent states.
Findings
Realization of gl(2,c) algebra on a sphere using vector operators
Construction of coherent states based on this algebra
Simplification of algebraic representation on spherical geometry
Abstract
By utilization of three elementary vector operators as position, angular momentum and their cross product, a simple realization of gl(2,c) Lie algebra on sphere are constructed. The coherent states based on this algebra can then be constructed by standard manner.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Quantum Mechanics and Non-Hermitian Physics · Algebraic structures and combinatorial models