论文标题
循环量子重力中任意自旋物质场的运动学
Kinematics of arbitrary spin matter fields in loop quantum gravity
论文作者
论文摘要
环量子重力设想了时空的小规模结构，该结构与经典的时空连续体明显不同。这对物质场的激发及其与重力的耦合产生了影响。人们对如何制定标量字段，旋转$ \ frac {1} {2} $字段和仪表字段中的旋转$ \ frac {1} {1} {2} $ clum量子重力框架有一般的了解。本工作的目的是研究该耦合的运动学方面。我们将研究Gauß和差异性限制对量子理论的含义：我们定义和研究Baez-Krasnov Pathable的含糊不清的变体，并研究通过平均差异群体施加的自旋网络状态的对称性特性。我们将在允许旋转$ \ frac {1} {2} $及更高的旋转激励的设置中执行此操作。对于Spin $ \ frac {1} {2} $，我们还将通过引入电磁场和反粒子来讨论其扩展。我们最终讨论了可以从更高自旋场的经典作用中获得高旋转的物质激发的图像。
Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity. There is a general understanding of how to formulate scalar fields, spin $\frac{1}{2}$ fields and gauge fields in the framework of loop quantum gravity. The goal of the present work is to investigate kinematical aspects of this coupling. We will study implications of the Gauß and diffeomorphism constraint for the quantum theory: We define and study a less ambiguous variant of the Baez-Krasnov path observables, and investigate symmetry properties of spin network states imposed by diffeomorphism group averaging. We will do this in a setting which allows for matter excitations of spin $\frac{1}{2}$ and higher. In the case of spin $\frac{1}{2}$, we will also discuss extensions of it by introducing an electromagnetic field and antiparticles. We finally discuss in how far the picture with matter excitations of higher spin can be obtained from classical actions for higher spin fields.
