Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On differential operators and unifying relations for $1$-loop Feynman
  integrands   We generalize the unifying relations for tree amplitudes to the $1$-loop
Feynman integrands. By employing the $1$-loop CHY formula, we construct
differential operators which transmute the $1$-loop gravitational Feynman
integrand to Feynman integrands for a wide range of theories, include
Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory,
Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory,
bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon
theory. The unified web at $1$-loop level is established. Under the well known
unitarity cut, the $1$-loop level operators will factorize into two tree level
operators. Such factorization is also discussed.

20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex