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Noise‐Tailored Constructions for Spin Wigner Function Kernels

Advanced Physics Research, Volume 3, Issue 6, June 2024.
This work explores the parameterization of spin Wigner functions to efficiently represent the effects of probabilistic unitary noise on a quantum state. Block diagonalization of the noise operator algebra is used to reduce the required number of parameters while maintaining the Stratonovich–Weyl conditions for the representation.
Michael Hanks, Soovin Lee, M.S. Kim
wiley +1 more source

Spin 1/2 one‐ and two‐particle systems in physical space without eigen‐algebra or tensor product

Mathematical Methods in the Applied Sciences, Volume 47, Issue 3, Page 1457-1470, February 2024.
Under the spin–position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra substitutes the vector–matrix spin model built on the Pauli spin operator. The standard quantum operator‐state spin formalism is replaced with vectors transforming by proper and improper rotations in the same 3D space ...
Sokol Andoni
wiley +1 more source

Some recent results for SU(3) and octonions within the geometric algebra approach to the fundamental forces of nature

Mathematical Methods in the Applied Sciences, Volume 47, Issue 3, Page 1471-1491, February 2024.
Different ways of representing the group SU(3)$$ SU(3) $$ within a Geometric Algebra approach are explored. As part of this, we consider characteristic multivectors for SU(3)$$ SU(3) $$ and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra.
Anthony Lasenby
wiley +1 more source

Clifford Algebras and Their Applications to Lie Groups and Spinors [PDF]