四阶微分方程的场论
Field Theory with Fourth-order Differential Equations
摘要：
引入了一类新的带有费曼传播子$\sim 1/p^4$的Higgs型复值标量场$U$，并从树级有效势的角度考虑了它与传统的带有传播子$\sim 1/p^2$的场的匹配问题.在对收敛性和因果性作了一些特殊假设的情况下，由场$U$产生了大量的势形式，如线性势、对数势和库仑势，它们可能是禁闭、暗能量、暗物质、电磁和引力等效应的来源。此外，在某些极限情形下，我们得到了一些推论，如：非线性Klein-Gordon方程，线性QED，具有生成结构的质量谱，规范对称性和味对称性的跷跷板机制，传播子$\sim 1/p^4$为构造可重整化引力理论和解决非微扰问题提供了一种可能的途径.
英文摘要：
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.
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