论文标题
真正的狄拉克方程
The Real Dirac Equation
论文作者
论文摘要
狄拉克（Dirac）的跳跃见解是，γ^μ矩阵的归一化抗强制性必须等于时间空间签名η^μν对于他的方程式的成功而言是决定性的。 γ^μ-S在所有Lorentz框架中都是相同的，并且“描述了一些新的自由度，属于电子中的某些内部运动”。因此，施加的与η^μν的联系构成了狄拉克理论的单独假设。我使用几何代数的形式主义从经典的4-Momentum矢量进行直接量化来得出一个明显的协变量方程。狄拉克电子和正电子的所有特性都遵循方程式 - 先入为主的“内部自由度”，临时施加的签名和矩阵不需要。在新的方案中，狄拉克操作员是没有框架的，显然是洛伦兹不变的。相对于洛伦兹框架，经典的时空框架向量e^μ而不是γ^μ矩阵。 3D方向空间的轴向框架向量（无交叉产物）定义自旋和旋转而不是Pauli矩阵； 3D位置空间的极性框架向量自然定义了提升，等等。与矩阵相比，形式主义的计算效率明显更高。
Dirac's leaping insight that the normalized anti-commutator of the γ^μ matrices must equal the timespace signature η^μν was decisive for the success of his equation. The γ^μ-s are the same in all Lorentz frames and "describe some new degrees of freedom, belonging to some internal motion in the electron". Therefore, the imposed link to η^μν constitutes a separate postulate of Dirac's theory. I derive a manifestly covariant first order equation from the direct quantization of the classical 4-momentum vector using the formalism of Geometric Algebra. All properties of the Dirac electron & positron follow from the equation - preconceived 'internal degrees of freedom', ad hoc imposed signature and matrices unneeded. In the novel scheme, the Dirac operator is frame-free and manifestly Lorentz invariant. Relative to a Lorentz frame, the classical spacetime frame vectors e^μ appear instead of the γ^μ matrices. Axial frame vectors (without cross product) of the 3D orientation space defining spin and rotations appear instead of the Pauli matrices; polar frame vectors of the 3D position space naturally define boosts, etc. Not the least, the formalism shows a significantly higher computational efficiency compared to matrices.
