Relativistic Landau and oscillator levels in a symmetric gauge field in a non-commutative complex space

• URL: http://arxiv.org/abs/2004.08687v1
• Date: Sat, 18 Apr 2020 18:47:03 GMT
• Title: Relativistic Landau and oscillator levels in a symmetric gauge field in a non-commutative complex space
• Abstract summary: It is shown that the relativistic Landau problem in a complex symmetric gauge field in a non-commutative complex space is similar to the Pauli equation in the presence of a symmetric gauge field in a commutative ordinary space. We show that the energy is not degenerate and is splitted into two levels, as in the Zeeman effect.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work we obtain the exact solution for relativistic Landau problem plus oscillator potential in a complex symmetric gauge field in a non-commutative complex space, using the algebraic techniques of creation and annihilation operators. It is shown that the relativistic Landau problem in a complex symmetric gauge field in a non-commutative complex space is similar behavior to the Pauli equation in the presence of a symmetric gauge field in a commutative ordinary space. We derive the exact non-commutative Landau and oscillator energy levels, while the non-relativistic limit of the energy spectrum is obtained. We show that the energy is not degenerate and is splitted into two levels, as in the Zeeman effect.

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