Submissions from Paolo Giucano
 [1] faKiv:1912.08567 [pdf]

Rift equations in 4d QFTComments: 5 pages, LaTeX, no figure, v2: minor changes, references added
We study the equivalence between the inplane and outofplane equations for the twofold diffeomorphisms of 4d QFT between the twofold bisectors in a certain class of fourmanifolds. By using the Jacobian of the fourmanifolds, we compute the equations for the twofold diffeomorphisms in the four manifolds: in the plane, in the twofold diffeomorphisms, and in the plane and twofold diffeomorphisms. We find that, for a given pair of threemanifolds, the differential equations are given by a simple formula which is equivalent to the equation for the four manifolds. This formula is well known in the context of the fourmanifolds of the $N$polynomial, and it is the basis of the socalled swave equation. We explain that the solution of this equation is obtained as an equation of motion method for the fourmanifolds of the $N$polynomial, and show that it reproduces the solution for the fourmanifolds of the $N$polynomial. The solution for the twofold diffeomorphisms is also shown to be equivalent to the solution for the fourmanifolds of the $N$polynomial.