Abstract : We discuss the general problem of symmetry beakdown in the algebraic approach to statistical mechanics. We consider in particular the case of classical quantum lattice systems.]]>
*) These notes are a result of discussions between S. Dpolicher, G. Gallavotti and D. Ruelle, they are not intended for publication.]]> 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.]]>
To Arkady Vainshtein on his 60th anniversary
]]> To appear in Reviews of Modern Physics.]]> 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.]]> 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.]]>
This paper will appear in part two of Symmetry in Nature, a volume in honour of Luigi Radicati di Brozolo, Sculoa Normale Superiore, Pisa, 1989]]>
Abstract : We introduce a new set of definitions of the fundamental concepts of n-dimensional crystallography. It is based on general properties of group actions. We also show how to determine the crystallographic system and the Bravais class of a cristallographic group.]]>
Abstract : An energy band in a solid contains an infinite number of states which transform linearly as a space group representation induced from a finite dimensional representation of the isotropy group of a point in space. A band representation is elementary if it cannot be decomposed as a direct sum of band representations; it describes a single band. We give a complete classification of the inequivalent elementary band representations.]]>