标题： 四维引力的显式协变正则量子化与微分同胚异常 显示英文标题

标题： Manifestly covariant canonical quantization of gravity and diffeomorphism anomalies in four dimensions

摘要： 引力的规范量子化需要了解其约束代数的表示理论，这在物理上等价于任意四维微分同胚的代数。 所有有趣的最低能量表示都是投影的，使得相关代数成为Virasoro代数的四维推广。 这种微分同胚异常在场论中是不可见的，因为相关的上循环是观察者在时空中的轨迹的泛函。 多维Virasoro代数在任意历史的相空间中自然作用，动力学扮演第一类约束的角色。 广义相对论通过将所有场在观察者的轨迹周围展开为泰勒级数，并在某个固定阶数处截断来正则化。 这种正则化但明显协变的理论在历史相空间中被量子化，之后再施加动力学，类似于BRST量子化。 当移除正则化时会出现无穷大；目前尚不清楚如何处理这些无穷大。 显示英文摘要

摘要： Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are projective, making the relevant algebra into a four-dimensional generalization of the Virasoro algebra. Such diffeomorphism anomalies are invisible in field theory, because the relevant cocycles are functionals of the observer's trajectory in spacetime. The multi-dimensional Virasoro algebra acts naturally in the phase space of arbitrary histories, with dynamics playing the role of first-class constraints. General relativity is regularized by expanding all fields in Taylor series around the observer's trajectory, and truncating at some fixed order. This regularized but manifestly general-covariant theory is quantized in the history phase space, and dynamics is imposed afterwards, in analogy with BRST quantization. Infinities arise when the regularization is removed; it is presently unclear how these should be dealt with.