Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n...Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.展开更多
It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics （QCD）. But hints of these features can also be observed at purely classic levels. For this purpose we need to find so...It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics （QCD）. But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang-Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the running of effective coupling constant, which is linear in the couplings both in the infrared and ultraviolet region.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11226066,11401155)Anhui Provincial Natural Science Foundation(No.1308085QA01)
文摘Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.
基金Supported by Beijing Municipal Natural Science Foundation under Grant No.Z2006015201001
文摘It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics （QCD）. But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang-Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the running of effective coupling constant, which is linear in the couplings both in the infrared and ultraviolet region.
