无质量标量场理论在Yang-Mills理论上的映射：经典情形
Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
摘要：
我们分析了最近提出的一个将无质量标量场理论映射到经典水平的杨-米尔斯理论的建议。可以看出，这种映射存在于微扰水平时，扩展是梯度扩展。在这个极限中，理论共享首阶的谱，即谐振子的谱。利用梯度展开，通过引入第五坐标并将理论转向欧几里得空间来保持洛伦兹协方差。这些展开式给出了标量场和杨-米尔斯场方程的共同解，这些解通过构造被证明存在，证实了杨-米尔斯场的所选分量确实是相应作用泛函的极值。
英文摘要：
We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of an harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.
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