The Integrability of Pauli System in Lorentz Violating Background
arXiv:0709.4276 · doi:10.1088/1126-6708/2008/01/039
Abstract
We systematically analyze the integrability of a Pauli system in Lorentz violating background at the non-relativistic level both in two- and three-dimensions. We consider the non-relativistic limit of the Dirac equation from the QED sector of the so-called Standard Model Extension by keeping only two types of background couplings, the vector a_mu and the axial vector b_mu. We show that the spin-orbit interaction comes as a higher order correction in the non-relativistic limit of the Dirac equation. Such an interaction allows the inclusion of spin degree non-trivially, and if Lorentz violating terms are allowed, they might be comparable under special circumstances. By including all possible first-order derivative terms and considering the cases a\ne 0, b\ne 0, and b_0\ne 0 one at a time, we determine the possible forms of constants of motion operator, and discuss the existence or continuity of integrability due to Lorentz violating background.
19 pages
References in corpus (22)
- Modern tests of Lorentz invariance
- Signals for Lorentz Violation in Post-Newtonian Gravity
- Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity
- Vacuum Cherenkov radiation
- Lorentz-Violating Electrostatics and Magnetostatics
- Lorentz-violating electrodynamics and the cosmic microwave background
- The Cherenkov effect in Lorentz-violating vacua
- Overview of the SME: Implications and Phenomenology of Lorentz Violation
- The Search for Quantum Gravity Signals
- Vacuum Cherenkov radiation and photon triple-splitting in a Lorentz-noninvariant extension of quantum electrodynamics
- Lorentz-violating corrections on the hydrogen spectrum induced by a non-minimal coupling
- Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics
- Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED
- Integrable and superintegrable quantum systems in a magnetic field
- Classical Solutions in a Lorentz-violating Scenario of Maxwell-Chern-Simons-Proca Electrodynamics
- The Casimir Force in a Lorentz Violating Theory
- A Remark on Lorentz Violation at Finite Temperature
- Lorentz Violation and Synchrotron Radiation
- Influence of Lorentz- and CPT-violating terms on the Dirac equation
- Integrable Hamiltonian systems with vector potentials
- Photon-propagation model with random background field: Length scales and Cherenkov limits
- Influence of Lorentz-violating terms on a two-level system
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- Lorentz and CPT tests with hydrogen, antihydrogen, and related systems
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- Geometric quantum phases from Lorentz symmetry breaking effects in the cosmic string spacetime
- Classical solutions for the Carroll-Field-Jackiw-Proca electrodynamics
- Second-order integrals for systems in involving spin