论文标题
离散的相位相对论Klein-Gordon和Dirac方程，以及新的非单明一角的Yukawa潜力
Discrete Phase Space-Continuous Time Relativistic Klein-Gordon and Dirac Equations, and a New Non-Singular Yukawa Potential
论文作者
论文摘要
本文介绍了离散相空间和连续时间的相互相对论效费和骨气场的第二次量化。数学公式涉及部分差异方程。开发了相应的Feynman图和新的$ S^{\＃} $ - 矩阵理论。在质子 - 普罗顿moller散射的特殊情况下，通过中性介子的交换，明确的二阶元素$ \ langle f | s^{\＃} _ {（2）} | i \ rangle $是推论的。在非常低的外部三摩米塔的近似中，明确衍生出$ \ langle f |明确衍生出新的Yukawa潜力。 s^{\＃} _ {（2）} | i \ rangle $。此外，严格证明这种新的Yukawa潜力无分歧。交换介子的质量参数可以设置为零，以在假设的费米子之间获得类型的标量玻色子交换。这提供了一种直接从新的无奇异性Yukawa潜力的新型库仑类型潜力的限制案例。在两个离散点，两个费米子之间的无差异库仑电位与Euler beta函数成正比。在这个相对论离散的相位连续时间内，显示单个量子占据了超托tori $ s^{1} _ {n^1} \ times s^{1} _ {n^3} _ {n^3} \ times s^{1} {1} _ {n^3} $ \ sqrt {2n+1} $。
This paper deals with the second quantization of interacting relativistic Fermionic and Bosonic fields in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. The corresponding Feynman diagrams and a new $S^{\#}$-matrix theory is developed. In the special case of proton-proton Moller scattering via an exchange of a neutral meson, the explicit second order element $\langle f | S^{\#}_{(2)} |i \rangle$ is deduced. In the approximation of very low external three-momenta, a new Yukawa potential is explicitly derived from $\langle f | S^{\#}_{(2)} |i \rangle$. Moreover, it is rigorously proved that this new Yukawa potential is divergence-free. The mass parameter of the exchanged meson may be set to zero to obtain a type of scalar Boson exchange between hypothetical Fermions. This provides a limiting case of a new Coulomb type potential directly from the new singularity free Yukawa potential. A divergence-free Coulomb potential between two Fermions at two discrete points is shown to be proportional to the Euler beta function. Within this relativistic discrete phase space continuous time, a single quanta is shown to occupy the hyper-tori $S^{1}_{n^1} \times S^{1}_{n^3} \times S^{1}_{n^3}$ where $S^{1}_{n}$ is a circle of radius $\sqrt{2n+1}$.
