标题： 多维Virasoro代数和量子引力 显示英文标题

标题： Multi-dimensional Virasoro algebra and quantum gravity

摘要： 我回顾了Virasoro代数的多维推广，即N维一般向量场代数vect(N)的非中心李代数扩张，以及它的Fock表示。作为背景独立理论如N维广义相对论的Noether对称性，该代数被认为与引力的量子化相关。为此，描述了更复杂的模块，这些模块以欧拉-拉格朗日方程的形式依赖于动力学。这些模块只有在时空为四维且同时存在玻色子和费米子时，才能明显被解释为量子场。 显示英文摘要

摘要： I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N-dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this end, more complicated modules which depend on dynamics in the form of Euler-Lagrange equations are described. These modules can apparently only be interpreted as quantum fields if spacetime has four dimensions and both bosons and fermions are present.