Applications of the nilpotent Dirac state vector
Peter Rowlands, J. P. Cullerne
幂零版本的狄拉克方程适用于重子波函数，强相互作用势，电弱混合，狄拉克和克莱因-戈登传播。结果被用来解释一个四元数矢量模型的颗粒结构。
The nilpotent version of the Dirac equation is applied to the baryon wavefunction, the strong interaction potential, electroweak mixing, and Dirac and Klein-Gordon propagators. The results are used to interpret a quaternion-vector model of particle structures.
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The nilpotent Dirac equation and its applications in particle physics
在以前的出版物中，幂零狄拉克形式主义已经被证明可以为粒子物理学的各个方面产生新的物理解释，并有可能计算标准模型中涉及的一些参数。到目前为止获得的应用程序进行了总结，与一些最近的事态发展的轮廓。
QED using the nilpotent formalism
在以前的论文中概述的狄拉克方程的幂零形式主义，适用于QED。它表明，通常被称为“重整化”是有效的事实，即幂零制定自动第二量子化和约束的字段到生产有限值的基本量的声明。
The Dirac algebra and its physical interpretation
狄拉克方程的一个版本是从第一原理使用四元数和多元4-向量的组合。所用算符的幂零形式使我们能够导出自由费米子、矢量玻色子、标量玻色子、玻色-爱因斯坦凝聚体和重子的波函数的显式表达式;湮灭、创造和真空算符;量子场积分; C、P和T变换;并对超对称性和重整化的意义提出新的见解。
Anderson's absolute objects and constant timelike vector hidden in Dirac matrices
安德森定理断言，相对论协变形式的动力学方程的对称性是由它的绝对对象的对称性决定的，应用于自由狄拉克方程。狄拉克矩阵是狄拉克方程唯一的绝对对象。狄拉克矩阵的变换有两种：（1）狄拉克矩阵是四维向量，波函数是标量;（2）狄拉克矩阵是标量，波函数是旋量。在第一种情况下狄拉克方程是非相对论性的，在第二种情况下它是相对论性的。将狄拉克方程转化为另一个标量-矢量变量，说明第一种转化方式是有效的，狄拉克方程不是相对论性的
Bound states of the one-dimensional Dirac equation for scalar and vector double square-well potentials
本文用转移矩阵方法解析研究了一维标量和矢量双方势阱Dirac方程的束缚态。对（1）矢量DSP、（2）标量DSP和（3）标量和矢量DSP幅值相等的三种情况下的本征值、波函数和密度概率进行了详细的数值计算。讨论了Dirac方程和薛定谔方程中情形（1）-（3）结果的异同。计算了波包的运动，研究了量子隧穿通过DSP中心势垒的过程。
We administered written free-response and multiple-choice questions and conducted individual interviews to investigate the difficulties that upper-level undergraduate and graduate students have with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations. We find that students share common difficulties with translating a state vector written in Dirac notation to the wave function in position or momentum representation.
Iterants, Fermions and the Dirac Equation
我们讨论基本的Clifford代数以及所有的矩阵代数和有限群的矩阵表示是如何来自迭代的：非常基本的过程，例如正负1的交替。....我们可以把-1的平方根看作一个时间迭代，一个A和B的乘积，其中A是.+-. B是时移算子。我们有AA = BB =1和AB + BA = 0，因此（AB）（AB）=-1。克利福德代数是（数学）世界的基础，费米子是由这些东西组成的。我们讨论了马约拉纳费米子的几何学和拓扑结构，我们讨论了狄拉克方程的结构，以及如何幂零和马约拉纳运营商自然出现在这种情况下。最后，我们在分裂四元数（迭代形式）的Majorana狄拉克方程在一维时间和三维空间的文件。
An efficient solution of the Dirac Hamiltonian flow equations has been proposed through a novel expandsion with the inverse of the Dirac effective mass. The efficiency and accuracy of this new expansion have been demonstrated by reducing a radial Dirac Hamiltonian with large scalar and vector potentials to two nonrelativistic Hamiltonians corresponding to particles and antiparticles, respectively. By solving the two nonrelativistic Hamiltonians, it is found that the exact solutions of the Dirac equation, for both particles and antiparticles, can be reproduced with a high accuracy up to only a …
On Dirac equation for a Coulomb scalar, vector, and tensor interaction
在他们最近的论文（国际米兰）。J. Mod. Phys. A 26（2011）1011），Zarrinklett和合著者考虑了库仑标量、矢量和张量相互作用的径向狄拉克方程。因此，他们报告的自旋对称性和赝自旋对称性的能量本征值的精确解处理不当，是不正确的本征值。
Symmetries and Supersymmetries of the Dirac Hamiltonian with Axially-Deformed Scalar and Vector Potentials
我们考虑几类对称的狄拉克哈密顿量在3+1维，轴向变形的标量和矢量的潜力。对称性包括已知的赝自旋和自旋极限以及当势依赖于不同变量时出现的额外对称性。超对称性观察到每个类和相应的费用确定。
The paper presents a new method of geometric solution of a Schrodinger equation by a construction of an equivalent first-order partial differential equation with a bigger number of variables. The equivalent equation shall be restricted to a specific subspace with auxiliary conditions which are obtained from a coherent state transform. The method is applied to the fundamental case of the harmonic oscillator and coherent state transform generated by the minimal nilpotent step three Lie group---the shear group (also known as quartic group in literature). We obtain a geometric solution for an arbi…
We find the exact bound-state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass function $m(x)$. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the non-relativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of $PT$-symmetr…
Supersymmetric Patterns in the Pseudospin Spin and Coulomb Limits of the Dirac Equation with Scalar and Vector Potentials
我们表明，狄拉克方程在3+1维引起超对称图案时的标量和矢量势（i）库仑与任意强度或（ii）当它们的和或差是一个常数，导致相对论性的赝自旋和自旋对称性。守恒量和共同的纠缠关系负责这种模式进行了讨论。
Dirac Equation with vector and scalar potentials via Supersymmetry in Quantum Mechanics
利用量子力学中超对称性的广义阶梯算符，研究了Dirac方程中由库仑势和Lorentz标量势组成的广义势描述的自旋$\frac 12$相对论粒子.这种形式适用于广义Dirac-Coulomb问题，这是相对论量子力学中的一个精确可解势。得到了基态和第一激发态的能量本征值和能量本征函数。
We point out a misleading treatment and incorrect expressions in a recent paper published in this Journal [Eur. Phys. J. C (2019) 79: 541] regarding solutions for the Dirac equation in presence of scalar and vector potentials in a class of flat Gödel-type space-time called Som-Raychaudhuri space-time. Following the appropriate procedure we obtain the solution for this system.
The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials for x>0 and x<0 cases.
We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, Pöschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional stationary equation is brought into the form of the Heun equation and its fundamental solutions are found as an irreducible combination of two Gauss hypergeometric functions. The energy spectrum and the scattering is studied in dependence on the conserved longitudinal momentum as well as on the strength of the coupling.
Dirac-Kahler equations on curved spacetimes
一个拉格朗日理论引起的版本的Dirac-Kahler方程的弯曲背景被认为是。主要的部分是一般的领域，有价值的代数的狄拉克矩阵，并满足一个狄拉克型方程。它们的分量是标量场、伪标量场、矢量场、轴向矢量场和场强，它们满足一阶Dirac-Kahler方程的不可约系统，该系统具有与平面情形类似的显著的规范和对偶性质。矢量场和轴向矢量场是产生场强的物理势，而标量场起辅助作用，可以通过固定合适的规范加以消除。场强度的手征分量对于Hodge对偶来说是自对偶的或反自对偶的。
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