Develops three complementary algebraic descriptions of 3D superintegrable quantum systems in magnetic fields using quadratic algebras, deformed-oscillator representations, and sl(2)/sl(3) Sturm algebraization to expose hidden symmetries.

#QuantumAlgebra #Superintegrability #Research

Algebraic methods reveal how Lie algebras directly solve quantum systems without differential equations, exposing hidden symmetries in harmonic oscillators, hydrogen atoms, and optical components.

#QuantumAlgebra #QuantumTheory #Research

Using polynomial algebra and deformed-oscillator methods, researchers derived the exact spectrum and complete representations for a three-dimensional oscillator with two coupled spin-1/2 particles.

#QuantumAlgebra #Superintegrability #Research

We present a unified factorization framework for driven anisotropic Rabi-Stark Hamiltonians using affine spin-pencil theory. The method yields exact zero-energy ground states and determines exceptional parameter values for finite-polynomial eigenstates.

#QuantumPhysics #QuantumAlgebra #Research

Unified algebraic framework reveals Holstein-Primakoff and Dyson-Maleev transformations emerge as factorizations of the same structure, bridging spin algebra and bosonic representations—advancing understanding of quantum magnetism, simulation, and computing.

#QuantumAlgebra #SpinBoson #Research

New obstruction theory for quantum cellular automata representations using algebraic K-theory spectrum. Develops universal obstruction classes for linearization problems and computes QCA spaces over key metric spaces.

#QuantumAlgebra #KTheory #Research

Proves that Clifford groups of multipartite quantum systems form natural semidirect products if and only if the Hilbert space dimension is not divisible by four, resolving a longstanding conjecture from classical mechanics.

#QuantumAlgebra #QuantumInformation #Research

Novel algebraic method enables direct construction of closed-form exponential unitaries mapping any pure quantum state to another, bypassing traditional basis-dependent approaches and scaling independently of Hilbert space dimension.

#QuantumInfo #QuantumAlgebra #Research

New algebraic framework defines parity operators for paraparticles via cubic relations. Parafermions+P generate so(2n+2); parabosons+P generate osp(2|2n). Parity spectrum {-p,...,p} links to Green's order of statistics, recovering standard parity at p=1.

#QuantumAlgebra #Parastatistics #Research

An update on Heisenberg and Kac-Moody categorification
Alistair Savage, Ben Webster et al.
Paper
Details
#HeisenbergKacMoody #QuantumAlgebra #CategorificationUpdate

Trace Formulas for Deformed W-Algebras
Fabrizio Nieri
Paper
Details
#DeformedWAlgebras #TraceFormulas #QuantumAlgebra