再论规范原理：走向时空和内部规范相互作用的统一
Revisited gauge principle: towards a unification of space-time and internal gauge interactions
摘要：
在时空对称性的量子观点下重新审视了最小耦合原理。这个修订是更好地实现了一个组的方法来量化（GAQ），其中组的上同调和扩展的群体发挥了主导作用。我们首先考虑电磁势的情况;伽利略群和/或庞加莱群被“局部”U（1）群（非中心）扩展。这个群也可以被看作是一个无限维群的中心扩展，由质量和电荷参数化，在这个群上，GAQ导致粒子在电磁场存在下运动的动力学。然后，我们通过把时空平移变成“局部的”来尝试粒子的引力相互作用。然而，将量子自由相对论粒子的真对称性的时空子群，即中心扩展的U（1）庞加莱群提升到“局部”，会导致一种新的纯引力起源的类电磁力。这是时空平移不是扩展庞加莱群的不变子群的结果，并构成了对时空和内部规范相互作用的非平凡混合的初步尝试。
英文摘要：
The minimal coupling principle is revisited under the quantum perspectives of the space-time symmetry. This revision is better realized on a Group Approach to Quantization (GAQ) where group cohomology and extensions of groups play a preponderant role. We firstly consider the case of the electromagnetic potential; the Galilei and/or Poincare group is (non-centrally) extended by the "local" U(1) group. This group can also be seen as a central extension, parametrized by both the mass and the electric charge, of an infinite-dimensional group, on which GAQ leads to the dynamics of a particle moving in the presence of an electromagnetic field. Then we try the gravitational interaction of a particle by turning into "local" the space-time translations. However, promoting to "local" the space-time subgroup of the true symmetry of the quantum free relativistic particle, i.e. the centrally extended by U(1) Poincare group, results in a new electromagnetic-like force of pure gravitational origin. This is a consequence of the space-time translations not being an invariant subgroup of the extended Poincare group and constitutes a preliminary attempt to a non-trivial mixing of space-time and internal gauge interactions.
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