Field Theory with Fourth-order Differential Equations

TL;DR

This paper introduces a new class of scalar fields with fourth-order propagators, exploring their potential to generate various fundamental interactions and addressing issues like confinement, dark energy, and quantum gravity.

Contribution

It proposes a novel scalar field framework with $1/p^4$ propagator, linking it to multiple physical phenomena and suggesting new approaches to quantum gravity and non-perturbative problems.

Findings

Generated potential forms include linear, logarithmic, and Coulomb.

Derived limits leading to nonlinear Klein-Gordon and linear QED.

Proposed $1/p^4$ propagator as a basis for renormalizable gravity.

Abstract

We introduce a new class of higgs type complex-valued 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 Klein-Gordon 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 non-perturbative problems.