Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of the invariant charge in massive theories with one
  coupling   Invariance under finite renormalization group (RG) transformations is used to
structure the invariant charge in models with one coupling in the 4 lowest
orders of perturbation theory. In every order there starts a RG-invariant,
which is uniquely continued to higher orders. Whereas in massless models the
RG-invariants are power series in logarithms, there is no such requirement in a
massive model. Only, when one applies the Callan-Symanzik (CS) equation of the
respective theories, the high-energy behavior of the RG-invariants is
restricted. In models, where the CS-equation has the same form as the
RG-equation, the massless limit is reached smoothly, i.e. the beta-functions
are constants in the asymptotic limit and the RG-functions starting the new
invariant tend to logarithms. On the other hand in the spontaneously broken
models with fermions the CS-equation contains a beta-function of a physical
mass. As a consequence the beta-functions depend on the normalization point
also in the asymptotic region and a mass independent limit does not exist
anymore.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph