Das Anadijiban, Chatterjee Rupak
Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada.
Department of Applied Physics, New York University, 2 MetroTech Center, Brooklyn, NY, 11201, USA.
Sci Rep. 2023 Nov 21;13(1):20356. doi: 10.1038/s41598-023-47344-w.
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 [Formula: see text]-matrix theory is developed. In the special case of proton-proton Møller scattering via an exchange of a neutral meson, the explicit second order element [Formula: see text] is deduced. In the approximation of very low external three-momenta, a new Yukawa potential is explicitly derived from [Formula: see text]. 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 [Formula: see text] where [Formula: see text] is a circle of radius [Formula: see text].
本文探讨在离散相空间和连续时间框架下相互作用的相对论费米子场和玻色子场的二次量子化。数学表述涉及偏微分方程。相应的费曼图和一种新的[公式：见原文]-矩阵理论得以发展。在通过中性介子交换进行质子 - 质子莫勒散射的特殊情况下，推导出显式的二阶元素[公式：见原文]。在极低外部三动量的近似下，从[公式：见原文]明确导出一种新的汤川势。此外，严格证明了这种新的汤川势是无散的。交换介子的质量参数可设为零，以得到假设费米子之间的一种标量玻色子交换类型。这直接从新的无奇点汤川势提供了一种新库仑型势的极限情况。两个离散点处的两个费米子之间的无散库仑势被证明与欧拉贝塔函数成正比。在这个相对论离散相空间连续时间内，单个量子被证明占据超环面[公式：见原文]，其中[公式：见原文]是半径为[公式：见原文]的圆。
