• Corpus ID: 248496226

Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space

  title={Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space},
  author={Horacio Falomir and Joaquin Liniado and Pablo Pisani},
. 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… 



On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra

Quantum phase transitions in the noncommutative Dirac Oscillator

We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the noncommutative plane. It is shown that the effect of non-commutativity is twofold: i) momentum non commuting

String theory and noncommutative geometry

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally

Quantum field theory on noncommutative spaces

Majorana Equation and Exotics: Higher Derivative Models, Anyons and Noncommutative Geometry

In 1932 Ettore Majorana proposed an inflnite-component relativistic wave equation for particles of arbitrary integer and half-integer spin. In the late 80s and early 90s it was found that the

Spin noncommutativity and the three-dimensional harmonic oscillator

A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics

Noncommutative quantum mechanics

We discuss the main features of noncommutative quantum mechanics, a version of nonrelativistic quantum mechanics that involves noncommuting coordinates. After finding a representation for the algebra

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-1/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle