Weyl几何中的世界线作用量
World-Line Actions in Weyl Geometry
浏览论文内容
中文总结 AI 辅助
本文从规范理论视角构造Weyl几何中类时曲线粒子的世界线作用量，发现对称相无满意固有时，自发对称破缺后可定义固有时，还构造了经典等价二次作用量。
中文摘要 AI 辅助
在本文中，我们从规范理论的视角，构造了Weyl几何中沿类时曲线运动的粒子的世界线作用量。所得作用量是无量纲的、Weyl不变的、可加的，且由于需添加一条开放Wilson线来描述一般Weyl场，该作用量通常是非局域的；在特殊情形下，该Wilson线可变为局域的，此时几何成为可积的。由于作用量无量纲，且理论的对称相中不允许引入质量参数，因此无法用该作用量来测量固有时。我们证明，定义固有时所需的通常条件（仿射参数化、时间量纲、可加性），结合Weyl不变性的要求，无法同时满足，故在对称相中不存在令人满意的固有时概念。在自发对称破缺下，粒子获得质量，作用量变为Riemannian，固有时可重新定义。我们还利用世界线上的einbein构造了一个经典等价的二次作用量，并表明非局域性源于对一个受约束场的积分。
英文摘要
In this note we construct, from a gauge theory perspective, the world-line action for a particle moving on a time-like curve in Weyl geometry. The action we find is dimensionless, Weyl invariant, additive and, in general, non-local due to an open Wilson line which we have to add in order to account for a general Weyl field. In special cases, this Wilson line can be local, but the geometry becomes integrable. The action can not be used to measure the proper time as it is dimensionless and no mass parameter is allowed in the symmetric phase of the theory. We show that the usual conditions for defining proper time: affine parametrization, dimension of time and additivity supplemented by the requirement of Weyl invariance can not be fulfilled simultaneously and therefore no satisfactory notion of proper time exists in the symmetric phase. Under spontaneous symmetry breaking the particle acquires a mass, the action becomes Riemannian and the proper time can be again defined. We also construct a classically equivalent quadratic action by using an einbein on the world-line and show that the non-locality can be seen to arise from integrating out a constrained field.
