标题： 相似性重整化群 显示英文标题

标题： The Similarity Renormalization Group

摘要： 量子场论需要一个截断来调节由局部相互作用引起的发散，然而物理结果不能依赖于这个截断的值。 重整化群采用一种变换，改变截断以分离产生与截断无关本征值的哈密顿量。 相似性重整化群基于相似变换，调节非对角矩阵元，迫使哈密顿量在截断降低时趋向于带对角形式。 这避免了传统作用于哈密顿量的变换所引发的病态，使得在渐近自由理论中能够产生一个行为良好的重整化哈密顿量微扰近似。 我们采用一个简单的二维δ函数例子来说明这种新的重整化技术。 显示英文摘要

摘要： Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the cutoff to isolate hamiltonians that produce cutoff-independent eigenvalues. The similarity renormalization group is based on similarity transformations that regulate off-diagonal matrix elements, forcing the hamiltonian towards a band-diagonal form as the cutoff is lowered. This avoids pathologies that plagued tradition transformations acting on hamiltonians, making it possible to produce a well-behaved perturbative approximation of renormalized hamiltonians in asymptotically free theories. We employ a simple two-dimensional delta function example to illustrate this new renormalization technique.