标题： QSD V：量子引力作为物质量子场论的自然调节器 显示英文标题

标题： QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories

摘要： 在物理学中有一个古老的猜想，即一旦成功地对引力场进行量子化，它应该作为背景度规下困扰量子场论的红外和紫外奇点的自然调节器。 我们证明了在这个连续体框架下的四维经典洛伦兹量子引力中，这个想法以一种精确的方式得到了实现。 具体来说，我们表明标准模型的哈密顿量支持一种表示，在这种表示中，围绕闭合环路的威尔逊环泛函以及沿着开线的泛函，其端点处有费米子和希格斯场插入，这些泛函是稠密定义的算符。 这个哈密顿量出人意料地没有任何奇点，它完全有限，无需重整化。 这一特性也存在于弦理论中。 然而与弦理论不同，我们处理的是标准模型与引力耦合的一个特定相，该相是完全非微扰定义的，并且是二阶量子化的。 显示英文摘要

摘要： It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized.