The Similarity Renormalization Group

Details The Similarity Renormalization Group The Similarity Renormalization Group

2000-09-06

arxiv.org/abs/hep-ph/0009071v1

Published in Quantum Field Theory, A 20th Century Profile

Physics

High Energy Physics

High Energy Physics - Phenomenology

28 pages, 7 postscript figures

Scientific paper

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.

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