Institute for Mathematical Physics on the Renormalization Group in Curved Spacetime on the Renormalization Group in Curved Spacetime
Institute for Mathematical Physics on the Renormalization Group in Curved Spacetime on the Renormalization Group in Curved Spacetime
复制标题
数学物理研究所弯曲时空重整化群 弯曲时空重整化群
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
R. Wald
中科院分区：
文献类型：
--
作者：
S. Hollands;R. Wald
我们定义了弯曲时空中可重整化相互作用量子场的重整化群流，通过它在时空度规g → λ 2 g标度下的行为。我们明确地考虑了标量场的情形，它的自相互作用形式为κ π 4，尽管我们的结果应该直接推广到其他可重整化的理论。我们构建的相互作用领域，以及其威克权力和他们的时间有序产品作为正式的权力系列在代数所产生的威克权力和时间有序产品的自由场，我们确定的变化，在相互作用领域的观测结果的变化所导致的重整化处方。我们的主要结果是证明了，对于任何固定的重整化规定，具有耦合参数p的时空（M，λ 2 g）的相互作用场代数同构于具有不同耦合参数值p（λ）的时空（M，g）的相互作用场代数。映射p → p（λ）产生重整化群流。定义了基本和非基本耦合参数的概念，我们定义了一个不动点的概念，作为一个点，p，在参数空间中，在重整化群流下的基本参数没有变化。
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, g → λ 2 g. We consider explicitly the case of a scalar field, ϕ, with a self-interaction of the form κϕ 4 , although our results should generalize straightforwardly to other renormalizable theories. We construct the interacting field—as well as its Wick powers and their time-ordered-products—as formal power series in the algebra generated by the Wick powers and time-ordered-products of the free field, and we determine the changes in the interacting field observables resulting from changes in the renormalization prescription. Our main result is the proof that, for any fixed renormalization prescription, the interacting field algebra for the spacetime (M, λ 2 g) with coupling parameters p is isomorphic to the interacting field algebra for the spacetime (M, g) but with different values, p(λ), of the coupling parameters. The map p → p(λ) yields the renormalization group flow. The notion of essential and inessential coupling parameters is defined, and we define the notion of a fixed point as a point, p, in the parameter space for which there is no change in essential parameters under renormalization group flow.