Title: Small Representation Principle Show Chinese title

Title: 小表示原理

Abstract: In a previous article Don Bennett and I looked for, found and proposed a game in which the Standard Model Gauge Group $S(U(2) \times U(3))$ gets singled out as the "winner". This "game" means that the by Nature chosen gauge group should be just that one, which has the maximal value for a quantity, which is a modification of the ratio of the quadratic Casimir for the adjoint representation and that for a "smallest" faithful representation. In a recent article I proposed to extend this "game" to construct a corresponding game between different potential dimensions for space-time. The idea is to formulate, how the same competition as the one between the potential gauge groups would run out, if restricted to the potential Lorentz or Poincare groups achievable for different dimensions of space-time $d$. The remarkable point is, that it is the experimental space-time dimension 4, which wins. It follows that the whole Standard Model is specified by requiring SMALLEST REPRESENTATIONS! Speculatively we even argue that our principle found suggests the group of gauge transformations and some manifold(suggestive of say general relativity). Show Chinese abstract

Abstract: 在之前的一篇文章中，唐·本内特和我寻找、发现并提出了一种游戏，在这种游戏中，标准模型规范群$S(U(2) \times U(3))$被选为“胜者”。 这个“游戏”意味着自然选择的规范群应该就是那个具有最大值的规范群，这个最大值是一个修改后的量，它是伴随表示的二次Casimir与一个“最小”忠实表示的二次Casimir的比值。 在最近的一篇文章中，我提议将这种“游戏”扩展到不同的时空维度之间。 其想法是阐述，如果将同一场竞争限制在不同时空维度下可实现的潜在洛伦兹或庞加莱群$d$之间，那么这场竞争会如何进行。 值得注意的是，实验确定的时空维度4是胜者。 这意味着整个标准模型是通过要求最小表示来确定的！ 推测性地，我们甚至认为我们的原理表明了规范变换群和某些流形（比如广义相对论所暗示的流形）。