Pauli Spin Matrices, Adjoint Matrix, and Hermitian Matrix

Hiu Yung Wong

Timothy Ganesan

In this work, a generalized analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit a general symmetry. The generalized spin projection operators are derived and the electrodynamics for hypothetical fermions are explored using the proposed spin matrices. The fermionic quantum Heisenberg model is constructed using the proposed spin matrices and comparative studies against simulation results using the Pauli spin matrices are conducted. Further analysis on key findings as well as discussions on extending the proposed spin matrix framework to describe hypothetical bosonic systems (spin-1) are provided.

Laurens Stronks, Johan W. van de Leur, Dirk Schuricht

Abstract Using the representation theory of Yangians we construct the rational R -matrix which takes values in the adjoint representation of SU( n ). From this we derive an integrable SU( n ) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.

Roderich Tumulka