Global conformal invariance in quantum field theory
Global conformal invariance in quantum field theory
复制标题
量子场论中的全局共形不变性
DOI：
10.1007/bf01608988
复制
发表时间：
1975
影响因子：
2.4
通讯作者：
G. Mack
中科院分区：
文献类型：
--
作者：
M. Lüscher;G. Mack
设给定一个Wightman量子场论，其欧氏绿色函数在欧氏共形群下是不变的。我们证明了它的物理态的希尔伯特空间带有闵可夫斯基共形群SOe（4，2）<$2的泛（∞-片化）覆盖群 * 的酉表示。Wightman函数可以解析地延拓到具有∞-片覆盖的真实的边界的全纯区域
$$\波浪线M$$
Minkowski空间M4已知 * 可以作用于这个空间
$$\波浪线M$$
并且
$$\波浪线M$$
承认一个全局 *-不变的因果序;
$$\波浪线M$$
因此，是一个全局 * 不变的局部QFT可以生存的自然空间。我们讨论了这类理论的一些性质，特别是共形Hamilton H =1/2（P0+ K 0）的谱，作为工具，我们使用了李半群的广义Hille-Yosida定理。这样的定理在附录C中陈述和证明。它使我们能够解析地继续某个极大子半群的压缩表示
$$\mathfrak{S}$$
的酉表示。
AbstractSuppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal group⋍SOe(5,1). We show that its Hilbert space of physical states carries then a unitary representation of the universal (∞-sheeted) covering group* of the Minkowskian conformal group SOe(4, 2)ℤ2. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an ∞-sheeted covering
$$\tilde M$$
of Minkowski-spaceM4. It is known that* can act on this space
$$\tilde M$$
and that
$$\tilde M$$
admits a globally*-invariant causal ordering;
$$\tilde M$$
is thus the natural space on which a globally*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal HamiltonianH=1/2(P0+K0).As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup
$$\mathfrak{S}$$
of to unitary representations of*.