Abstract. - Topologically stable symmetry defects in ordered media can be classified by some homotopy groups. As an example we establish a complete classification of such defects for crystals.]]>
Abstract : This paper studies the number of extrema (and their positions) of a countinuous Morse function on the Brillouin zone, when it is invariant by the point group symmetry of the crystal. Forty years ago, Vanhove had shown the importance of this problem in physics, but he could use only the crystal translational symmetry. In that case Morse theory predicts at least eight extrema. With the added use of general symmetry arguments we show that this number is larger for six of the 14 classes of Bravais lattices ; moreover it is possible to give the position of the extrema (and their nature) for 30 of the 73 arithmetic classes.This paper is written for a larger audience than that of solid state physicists ; it also defines carefully the necessary crystallographic concepts which are generally poorly understood in the solid state literature.]]> 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.]]>