The integrability of Pauli system in Lorentz violating background


Frank M., Turan I., Yurdusen İ.

JOURNAL OF HIGH ENERGY PHYSICS, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

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 at, 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 not equal 0, b not equal 0, and b(0) not equal 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.