# Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space

@inproceedings{Falomir2022AlgebraicSO, title={Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space}, author={Horacio Falomir and Joaquin Liniado and Pablo Pisani}, year={2022} }

. In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspec-tive. In order to do so, we consider the graded Lie algebra sl (2 | 1) generated by Hermitian bilinear forms in the non-commutative dynamical variables and the Dirac matrices in 2 + 1 dimensions. By further deﬁning a total angular momentum operator, we are able to express a class of Dirac Hamiltonians completely in terms of these operators. In this way…

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