Algebraic structure of Dirac Hamiltonians in non-commutative phase space
Algebraic structure of Dirac Hamiltonians in non-commutative phase space
Abstract In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra <?CDATA $\mathfrak{sl}(2|1)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="fraktur">s</mml:mi> <mml:mi mathvariant="fraktur">l</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> <mml:mo …