Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neutrino-(anti)neutrino forward scattering potential for massive
  neutrinos at low energies   In this work, we calculate expression for the potential due to
neutrino-(anti)neutrino forward scattering at low energies ($E<<m_{Z^0}$) for
ultra-relativistic massive neutrinos ($E>>m_{\nu}$), a representative regime
within astrophysical scenarios. There is a broadly used expression for this
potential in the literature, which, however, lacks an explicit derivation from
basic principles of quantum field theory. Therefore, this paper has the
intention to guide the reader through the steps and concepts to derive this
potential, trying to be clear and pedagogical. Moreover, we used a rigorous
approach concerning the massive nature of the neutrinos, using massive
quantized neutrino fields throughout the entire process, while the usual
approach is to consider massless neutrino fields at the interaction. In this
context, we explicitly show the validity of the massless neutrino fields
approximation at the ultra-relativistic regime, as expected. As the last step,
we connect the potential expression to the density matrix formalism, which is a
usual framework for works considering neutrino-neutrino interactions. We also
discuss some theoretical details through the paper, such as the normal ordering
of quantum operators and the implications of massive fields in the neutrino
state at its production.

20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th