二维Dirac方程中的Higgs代数对称性

Dirac, Bohm and the Algebraic Approach

In this paper we show how Dirac, in 1947, anticipated the Bohm approach using an argument based on what is now called the Heisenberg picture. From a detailed examination of these ideas, we show that the role played by the Dirac standard ket is equivalent to the introduction and use of the idempotent in the orthogonal and symplectic Clifford algebras. This formalism is then used to show that the so-called `Bohm trajectories' are the average of an ensemble of individual stochastic Feynman paths. Since the Bohm approach can be simply reduced to classical mechanics, the algebraic formalism present…

Algebraic solution and coherent states for the Dirac oscillator interacting with the Aharonov-Casher system in the cosmic string background

We introduce an $SU(1,1)$ algebraic approach to study the $(2+1)$-Dirac oscillator in the presence of the Aharonov-Casher effect coupled to an external electromagnetic field in the Minkowski spacetime and the cosmic string spacetime. This approach is based on a quantum mechanics factorization method that allows us to obtain the $su(1,1)$ algebra generators, the energy spectrum and the eigenfunctions. We obtain the coherent states and their temporal evolution for each spinor component of this problem. Finally, for these problems, we calculate some matrix elements and the Schrödinger uncertainty…

关于从Maxwell-Dirac电动力学中消除旋量场的可能性

On the possibility of differential-algebraic elimination of the spinor field from the Maxwell--Dirac electrodynamics

研究在特定规范下Maxwell-Dirac方程中旋量场能否通过微分-代数方法消除，通过构造截断幂级数解并线性化延长系统，分析系数矩阵的秩，发现电磁场及其导数可唯一确定旋量场，电磁四势的四阶时间导数也由低阶导数决定，表明旋量场可被消除，电磁场可独立演化。

Dirac电子定域和运动的量子代数表示

Quantum algebraic representation of localization and motion of a Dirac electron

定义了表示狄拉克电子在时空中局域化的量子代数观测量。电子的惯性运动用量子代数表示，电子质量作为运动的发生器。由于对匀加速标架的变换自然包含在这种共形不变描述中，量子代数也能够处理匀加速运动。

自旋和赝自旋对称性下弯曲时空中修正狄拉克振子的代数方法与相干态

Algebraic Approach and Coherent States for the Modified Dirac Oscillator in Curved Spacetime with Spin and Pseudospin Symmetries

该研究采用代数方法精确求解弯曲时空中带自旋与赝自旋对称性的修正狄拉克振子，通过薛定谔因式分解法证明其SU(1; 1)对称性，得到波函数与能谱，并算出两类极限下的径向相干态及时间演化。

二维Dirac费米子的电子分数化

Electron fractionalization for two-dimensional Dirac fermions

最近，在描述大质量狄拉克费米子、轴向规范荷为2的复值希格斯场和U（1）轴向规范场之间耦合的$(2+1)$维时空场论中，证明了不破坏时间反演对称性的费米子数分数化。当希格斯场本身支持涡旋时，或者当这些涡旋伴随着轴向规范场中的半涡旋时，电荷分馏就会发生。分数电荷是通过三种不同的技术计算的。分数电荷的公式作为一个函数的狄拉克哈密顿量，打破了光谱能量反射对称性的参数。在希格斯场中只存在电荷$\pm1$涡旋时，分数电荷连续变化，因此可以取无理值。轴向规范场的半涡旋和希格斯场中的电荷$\pm1$涡旋的同时存在将分数电荷重新合理化为1/2。