物理与工程

本文从量子力学中的费米黄金规则出发,用与量子力学相对应的概念来描述粒子衰变宽度和散射截面等场论基本概念,并建立了这些概念之间的关系。通过分析含时微扰论的跃迁率,阐明了跃迁矩阵元与态密度在粒子衰变与散射过程中的物理意义,利用相空间积分形式推导出相对论协变的衰变宽度与散射截面公式。论文进一步探讨了一维空间中粒子衰变和散射的简化模型,通过一个包含三个标量粒子相互作用的简单拉氏量,具体计算展示了场论中粒子散射的运动学与动力学特征。论文有助于学习者从量子力学自然过渡到量子场论框架中,对理解对撞机物理具有启发意义。

This paper commences with the Fermi's Golden Rule in quantum mechanics, employing concepts corresponding to quantum principles to elucidate fundamental notions in field theory such as particle decay widths and scattering cross-sections. It further establishes the intrinsic relationships among these concepts. By analyzing the transition rate under time-dependent perturbation theory, the physical meaning of the transition matrix element and density of states in decay and scattering processes is elucidated. Furthermore, this paper also shows the relativistically covariant formulas for decay width and scattering cross-section by using phase-space integral formulations. A simplified model, which describes interactions among three scalar particles, is constructed for a demonstration of particle decay and scattering in one-dimensional space. This approach intuitively reveals the kinematic and dynamic characteristics of particle scattering. It facilitates a natural transition for learner from quantum mechanics to the framework of quantum field theory, offering instructive insights for understanding collider physics.