Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple Applications of Effective Field Theory and Similarity
  Renormalization Group Methods   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.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys