Field Theory with Fourthorder Differential Equations
Abstract
We introduce a new class of higgs type complexvalued scalar fields $U$ with Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at tree level. With some particular postulations on the convergence and the causality, there are a wealth of potential forms generated by the fields $U$, such as the linear, logarithmic, and Coulomb potentials, which might serve as sources of effects such as the confinement, dark energy, dark matter, electromagnetism and gravitation. Moreover, in some limit cases, we get some deductions, such as: a nonlinear KleinGordon equation, a linear QED, a mass spectrum with generation structure and a seesaw mechanism on gauge symmetry and flavor symmetry; and, the propagator $\sim 1/p^4$ would provide a possible way to construct a renormalizable gravitation theory and to solve the nonperturbative problems.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.13514
 Bibcode:
 2020arXiv200713514L
 Keywords:

 Physics  General Physics;
 High Energy Physics  Theory
 EPrint:
 24 pages, 2 figures