**Authors:** Rui-Cheng LI

We introduce a new class of higgs type fields $\{U,U^{\mu},U^{\mu\nu}\}$ with Feynman propagator $\thicksim 1/p^4$, and consider the matching to the traditional gauge fields with propagator $\thicksim 1/p^2$ in the viewpoint of effective potentials at tree level. With some particular restrictions on the convergence, there are a wealth of potential forms generated by the fields $\{U,U^{\mu},U^{\mu\nu}\}$, such as: (1) in the case of $U$ coupled to the intrinsic charges of matter fields, electromagnetic Coulomb potential with an extra linear potential and Newton's gravitation could be generated with the operators of different orders from the dynamics of $U$, respectively; (2) for the matter fields, with the multi-vacuum structure of a sine-Gordon type vector field $A^{\mu}$ induced from $U$, a seesaw mechanism for gauge symmetry and flavor symmetry of fermions could be generated, in which the heavy fermions could be produced; besides, by treating the fermion current as a field, a possible way for renormalizable gravity could be proposed; (3) the Coulomb potential in electromagnetism and gravitation could be generated by an anti-symmetric field strength of $U^{\mu}$, when it's coupled to the intrinsic charge and momentum of matter fields, respectively; and, except for the Coulomb part in each case, there is a linear and a logarithmic part in the former case which might correspond to the confinement in strong QED, while there is a linear and a logarithmic part in the latter case which might correspond to the dark energy effects in the impulsive case and dark matter effects in the attractive case, respectively; besides, a symmetric field strength of $U^{\mu}$ could also generate the same gravitation form as the anti-symmetric case; (4) a nonlinear version Klein-Gordon equation, QED and the Einstein's general relativity, could be generated as a low energy approximation of the dynamics of $U$, $U^{\mu}$ and $U^{\mu\nu}$, respectively; moreover, in the weak field case, the gauge symmetry could superficially arise, and, a linear QED, linear gravitation and a 3rd-order tensor version QED could be generated by relating the field strength of $U$, $U^{\mu}$ and $U^{\mu\nu}$ to the corresponding gauge fields, respectively; (5) for the massive $\{U, U^{\mu}\}$, attractive potentials for particles with the same kind of charges could be generated, which might serve as candidate for interactions maintaining the s-wave pairing and d-wave pairing Cooper pairs in superconductors, with electric charge in the $U$ case and magnetic moment in the $U^{\mu}$ case as interaction charge, respectively; etc.

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[v1] 2017-12-17 05:32:41

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