Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1999-06-10
Physics
Nuclear Physics
Nuclear Theory
LATEX with 14 figures, submitted to Annals of Physics
Scientific paper
We use two renormalization techniques, Effective Field Theory and the Similarity Renormalization Group, to solve simple Schr{\"o}dinger equations with delta-function potentials in one and two dimensions. The familiar one-dimensional delta-function does not require renormalization, but it provides the simplest example of a local interaction that can be replaced by a sequence of effective cutoff interactions that produce controllable power-law errors. The two-dimensional delta-function leads to logarithmic divergences, dimensional transmutation and asymptotic freedom, providing an example of some of the most important renormalization problems in gauge field theories. We concentrate on the power-law analysis of errors in low-energy observables. The power-law suppression of the effects of irrelevant operators is critical to the success of field theory, and understanding them turns renormalization group techniques into powerful predictive tools for complicated problems where exact solutions are not available.
Perry Robert
Szpigel Sergio
No associations
LandOfFree
Simple Applications of Effective Field Theory and Similarity Renormalization Group Methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Simple Applications of Effective Field Theory and Similarity Renormalization Group Methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Simple Applications of Effective Field Theory and Similarity Renormalization Group Methods will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-199637