Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The thermal and kinematic Sunyaev-Zel'dovich effects revisited   This paper shows that a simple convolution integral expression based on the
mean value of the isotropic frequency distribution corresponding to photon
scattering off electrons leads to useful analytical expressions describing the
thermal Sunyaev-Zel'dovich effect. The approach, to first order in the Compton
parameter is able to reproduce the Kompaneets equation describing the effect.
Second order effects in the parameter $z=\frac{kT_{e}}{mc^{2}}$ induce a slight
increase in the crossover frequency.

34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat