We calculate it now in the hope that it might be of help to the readers of the accompanying paper on SU(3)xSU(13) where the same formalism is used to discuss some physically interesting problems.
We believe that the geometrical approach presented in these papers will help clarifying the relations and the properties of the fundamental interactions.
It might be used for example to understand the geometrical basis of some recent attempts to compute Cabibbo's angle.]]> Last time I came to Sweden, cars were drivent on the left side of the roads. This week most cars I saw were driven on the right side. I am very grateful to the Nobel Foundation for this opportunity to observe this P violation. I may have found the cause of this P violation by looking at buses or trucks with the same inscription on both sides ; they are not symmetrically written.
I have also made a couter-experiment to verify this theory. In Tokyo I found an equal probability for cars to be driven on the left side or the right side of the streets and I did observe that identical texts were placed symmetrically on buses and trucks : the first character is near the front part on both sides so the same text must be read from left to right on one side and from right to left on the other side.
Since I have never been yet in a car undergoing a spontaneous CP transformation, I will be able to give you today my report on CP, T and CPT invariance.]]> This result is applied to discuss charged systems and stability is proved for Coulomb interactions if the charges are somewhat smeared rather than concentrated at points. For a large class of potentials it is shown that classical instability implies quantum instability in the case of bosons and, in three or more dimensions, also of fermions. Quantum systems with Coulomb interactions (point charges) are discussed and it is shown in particular that their stability cannot depend on the ratios between the masses of the particles.]]>
Abstract : For systems with a symmetry group G, the description of physical phenomena corresponding to a representation of G, depends only on the image of this representation.The classification of the images of the unirreps (unitary irreductible representations) of the little space groups Gk is remarkably simple. The nearly four thousands inequivalent unirreps corresponding to high symmetry wave vectors k have only 37 inequivalent images.]]> Finally counter examples, with v arbitrarily large, are given to the Dzyaloshinskii conjecture that there exist no stable fixed points when the Landau potential depends on more than V = 3 parameters. ]]>