Commutative Relations for the Nonlinear Dirac Equation
نویسنده
چکیده
By constructing the commutative operators chain, we derive conditions for solving the eigenfunctions of Dirac equation and Schrödinger type equation via separation of variables. Detailed calculation shows that, only a few cases can be completely reduced into ordinary differential equation system. So the effective perturbation or approximation methods for the resolution of the spinor equation are necessary, especially for the nonlinear cases. PACS numbers: 02.30.Ik, 02.30.Jr, 03.65.-w, 11.30.-j
منابع مشابه
Noncommutative Monopole from Nonlinear Monopole
We solve the non-linear monopole equation of the Born-Infeld theory to all orders in the NS 2-form and give physical implications of the result. The solution is constructed by extending the earlier idea of rotating the brane configuration of the Dirac monopole in the target space. After establishing the non-linear monopole, we explore the non-commutative monopole by the Seiberg-Witten map. ∗mor...
متن کاملAn Integrable Evolution Equation in Geometry
We introduce an integrable Hamiltonian system which Lax deforms the Dirac operator D = d + d∗ on a finite simple graph or compact Riemannian manifold. We show that the nonlinear isospectral deformation always leads to an expansion of the original space, featuring a fast inflationary start. The nonlinear evolution leaves the Laplacian L = D invariant so that linear Schrödinger or wave dynamics i...
متن کاملGravity coupled with matter and the foundation of non commutative geometry
We rst exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its in nitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = | = D 1 where D is the Dirac operator. We extend these simple relations to the non commutative case using Tomita's involut...
متن کاملبررسی نوسانگرهای کلاین-گوردن و دیراک در فضای ناجابهجایی تحت میدان مغناطیسی ثابت
In this paper the Klein-Gordon and the Dirac Oscillators in a non-commutative space and in a constant magnetic field are investigated. It is shown that for a specific value of the magnetic field, one may map these oscillators from a non-commutative space to a commutative space.
متن کاملThe Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries
We show that Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincaré covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We presen...
متن کامل