A Jordanian quantum two-photon/Schrodinger algebra

Abstract

A non-standard quantum deformation of the two-photon algebra $h_6$ is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock-Bargmann realizations that provide a direct formalism for the definition of deformed states of light. Finally, the isomorphism between $h_6$ and the (1+1) Schrödinger algebra is used to introduce a new (non-standard) Hopf algebra deformation of this latter symmetry algebra.

12 pages, LaTeX, misprints corrected

References in corpus (6)

• Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing
• Universal $R$-matrix for non-standard quantum $sl(2,\mathbb{R})$
• Irreducible Representations of Jordanian Quantum Algebra ${\mathcal{U}}_h(sl(2))$ Via a Nonlinear Map
• Boson representations, non-standard quantum algebras and contractions
• Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras
• On ${\mathcal{U}}_h(sl(2))$, ${\mathcal{U}}_h(e(3))$ and their Representations

Cited by in corpus (10)

• (Super)integrability from coalgebra symmetry: formalism and applications
• (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
• Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
• N-dimensional integrability from two-photon coalgebra symmetry
• Poisson-Hopf deformations of Lie-Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra
• A representation-theoretical approach to higher-dimensional Lie-Hamilton systems: The symplectic Lie algebra $\mathfrak{sp}(4,\mathbb{R})$
• Twist of Lie algebras by 6 dimensional subalgebra
• Casimir operators induced by Maurer-Cartan equations