论文标题
小波的晶格量子场的缩放限制
Scaling limits of lattice quantum fields by wavelets
论文作者
论文摘要
我们为晶格量子场理论提供了严格的重新规范化组方案，该方案就运算符代数而言。重新归一化组被认为是晶格场代数之间缩放图的电感系统。我们使用Daubechies的小波构建标量晶格场的缩放图，并表明存在游离晶格基态的电感极限，并且极限状态延伸至熟悉的大规模连续性无效场，并具有时空翻译的连续性作用。特别是，晶格场是用Daubechies的缩放函数涂抹的连续性场识别的。我们将缩放图与其他重新归一化方案及其特征进行比较，例如动量壳方法或块旋转转换。
We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies' wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies' scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations.
