On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature

Solution of Dirac Equation for Charged and Neutral Fermions with Anomalous Magnetic Moments in Uniform Magnetic Field

The Dirac equation for charged and neutral fermions with anomalous magnetic moments is solved in a uniform magnetic field. We find the relativistic wave functions and energy spectra. In the non-relativistic limit the wave functions and energy spectra of charged fermions agree with the known solutions of the Schroedinger equation.

Comparison of two formulas for metric connections in the bundle of Dirac spinors

Two explicit formulas for metric connections in the bundle of Dirac spinors are studied. Their equivalence is proved. The explicit formula relating the spinor curvature tensor with the Riemann curvature tensor is rederived.

Analyticity and uniform stability in the inverse spectral problem for Dirac operators

We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly stable in a certain sense.

非均匀磁场下石墨烯中 Dirac 电子的 Landau 能级

Landau levels of a Dirac electron in graphene from non-uniform magnetic fields

针对石墨烯中 Dirac 电子的 Landau 能级问题，本文基于 Dirac 哈密顿量，通过均匀磁场的等谱形变，给出了与均匀磁场严格等谱的非均匀磁场解析表达式，证明非均匀磁场也能支持 Landau 能级。

度量仿射时空中的广义狄拉克方程

Generalized Dirac Equation in Metric-Affine Spacetimes: Consistency, Effective Mass, and Spinor Curvature

本文提出在度量仿射时空中的广义狄拉克方程，通过两种方法推导并验证其一致性，发现新项对旋量质量产生影响。

A self consistent solution to the Einstein Maxwell Dirac Equations

A self consistent solution to Dirac equation in a Kerr Newman space-time with $M^2 > a^2 + Q^2$ is presented for the case when the Dirac particle is the source of the curvature and the electromagnetic field. The solution is localised, continuous everywhere and valid only for a special choice of the parameters appearing in the Dirac equation.

Conformal invariants of twisted Dirac operators and positive scalar curvature

For a closed, spin, odd dimensional Riemannian manifold $(Y,g)$, we define the rho invariant $ρ_{spin}(Y,E,H, g)$ for the twisted Dirac operator $D^E_H$ on $Y$, acting on sections of a flat hermitian vector bundle $E$ over $Y$, where $H = \sum i^{j+1} H_{2j+1}$ is an odd-degree closed differential form on $Y$ and $H_{2j+1}$ is a real-valued differential form of degree ${2j+1}$. We prove that it only depends on the conformal class of the pair $[H,g]$. In the special case when $H$ is a closed 3-form, we use a Lichnerowicz-Weitzenbock formula for the square of the twisted Dirac operator, to show …

具有常数负曲率表面的 Dirac Landau 能级

Dirac Landau levels for surfaces with constant negative curvature

本文扩展先前工作，研究了伪球面 Dirac 方程在垂直与同轴磁场下的解析解，发现同轴磁场下 Landau 能级劈裂并呈现 $\propto B^{1/4}$ 的特殊标度，不同于平面的线性或 $B^{1/2}$ 依赖。

Nonlinear Dirac equations, Monotonicity Formulas and Liouville Theorems

We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.

Gauss-Bonnet for matrix conformally rescaled Dirac

We derive an explicit formula for the scalar curvature over a two-torus with a Dirac operator conformally rescaled by a globally diagonalizable matrix. We show that the Gauss-Bonnet theorem holds and extend the result to all Riemann surfaces with Dirac operators modified in the same way.