Argone summer study High energy physics with polarized beams
Talk given by Louis Michel at the Workshop Acceleration and storage of Polarized Beams (July 25, 1974)
Analysis of polarization measurements and test of selection rules and of models
Summer Study : High Energy with Polarized Beans, Argonne National Laboratory. Talk of Louis Michel (July 25, 1974)
Simple mathematical models of symmetry breaking. Application to particle physics. Conference given on March 26, 1974 at the Warsaw Symposium in Mathematical Physics
Some Remarks on polarization measurement and polarization domain
Abstract : We emphasize that any analysis of polarization measurement must be done in terms of the polarization domain which is much smaller than the domain of physical bounds. We propose a possible quantitative procedure to estimate the precision of a measurement and its compatibility with the positivity condition. We illustrate our discussion with the case of spin-32particles and as an application we study some experimental results on Y? (1385).
Constraints on spin rotation parameters due to isospin conservation
Abstract : We made a complete study of the relations between the three cross sections and the three sets of spin rotation parameters P, A, R for three reactions related by internal symmetry via two channels.
Geometrical properties of the fundamental interaction. Lecture presented by the first author on September 19, 1969 at the Convegno Mendeleviano in Roma
The Group of automorphisms of the Poincaré group
Sur les Extensions centrales du groupe de Lorentz inhomogène connexe
Symmetry and topology of energy bands in crystals
Lecture given at the internation schoolon Symmetry abd Structural Properties of Condensed Matter. August 27 - September 2, 1998, Zajaczkowo (Posnan), Poland.
Recent results on the implications of crystal symmetry and time reversal
Lecture given on August 1rst 1997 at the VIIIth International Conference on Symmetry Methods un Physics. JINR, Dubna, Russia.
Rydberg states of atoms and molecules. Basic group theoretical and topological analysis
Abstract : Rydberg states of atoms and molecules are studied within the qualitative approach-based primarily on topological and group theoretical analysis. The correspondence between classical and quantum mechanics is explored to apply the results of qualitative (topological) approach to classical mechanics developed by Poincaré, Lyapounov and Smale to quantum problems. The study of the action of the symmetry group of the problems considered on the classical phase space enables us to predict qualitative features of the energy level patterns for quantum Rydberg operators.
Complete description of the Voronoï cell of the Lie Algebras An weight lattice. On the Bounds for the number of d-faces of the n-dimensional Voronoï cells
Version étendue d'une conférence faite le 9 janvier 1997 au Centre de Recherches Mathématiques de l'Université de Montréal au cours du colloque pour le 60e anniversaire de Jiri Patera et Pavel Winternitz. Abstract :Denoting these bounds by Nd(n), 0 ? d ? n we prove that Nd(n)/(n + 1)! is a polynomial Pd(n) of degree d with rational coefficients. We give the polynomials for d ? 5 explicitly. The proof uses the fact that these bounds Nd(n) are also the number of d-faces of the Voronoï cell of the weight lattice of the Lie algebra An (it is also the Cayley diagram of the symmetric group Sn+1, which is isomorphic to the Weyl group of An). Each d-face of this cell is a zonotope that can be defined by a symmetry group ~ G d (?), (d-dimensional reflection subgroup of the A n Weyl group. We show that for a given d and n large enough, all such subgroups of A n are represented, and we compute explicitly N(G d (?),n) the number of d-faces of type G d (?) in the Voronoï cell of L = A w n. The final result is obtained by summing over a. That also yields the simple expression Nd(n)=(n+1?d)!S(n+1?d)n+1Nd(n)=(n+1?d)!Sn+1(n+1?d) where the last symbol is the Stirling number of second kind.
Lecture given at Goslar (Germany) on july 16, 1996 to close the Wigner award ceremony during the 21st International Colloquium on Group Theoretical Methods in Physics
Physical implications of crystal symmetry and time reversal
Lectures given at the international school on Symmetry and Structural Properties of Condensed Matter. August 28 - September 5, 1996, Zajaczkowo (Posnan), Poland.
Collapse of the Zeeman structure of the hydrogen atom in external electric field
Abstract : From Zeeman to Stark structure of a weakly split Rydberg n multiplet of the H atom in parallel magnetic and electric fields is analyzed. Classical mechanics together with topologiacl and group theoretical arguments enable us to describe in details the modifications of dynamics under the variation of electric field near the point where the collapse of magntic Zeeman structure is observed. Sequence of classical bifurcations responsible for the transition between different dynamic regimes is given. Comparison with quantum picture is done.
Bravais classes, Voronoï cells, Delone symbols
This text correspond to a set of lectures given at Third international school at Zajaceskowo (Poznan) Polane on Symmetry and structural Properties of condensed matter Abstract : We give the most refined intrinsic classification of three dimensional Euclidean lattices by combining the 14 Bravais classes, the 5 combinatorial types of Voronoï cells and the 24 Delone symbols. After recalling the fondamental concepts of group actions, we define Bravais classes and Voronoï celles in arbitrary dimension. We are quite explicit for the application to two and three dimensions.
D-E classification of the local extensions of su 2 current algebras
Abstract : A method is developed for constructing single valued rational 4-point functions of primary fields for su2 conformal current algebra satisfying the Knizhnik-Zamolodchikov equation. For integer conformal dimensions ? these rational solutions are proven to be in one-to-one correspondence with non-diagonal modular invariant partition functions of the D-even and E-even series of the ADE classification.
Extrema of P-invariant functions on the Brillouin zone
Exapnded version of a lecture fiven at Naples, on October 25, 1991 at a Colloquium in memory of Léon Vanhove 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.
Classification of the symmetries of ordinary differential equations
Conference given at the XIIIth International Colloquium on Group Theoretical Methods in Physics. Moscow, june 4-9, 1990 Abstract : We present S. Lie's work on the symmetry of ODE (ordinary differential equations) : action of Diff 2(x,y), the Lie algebra of vector fields of the plane x, y, on the set of ODE ; general form of ODE with a given symmetry algebra ; computation of the symmetry algebra of a given equation. The original part of this conference studies the general linear equation of order n>2 (this has also be done independenty by Mohamed and Leach, ref. [9]). We also present in a more precise form the work of Lie on the finite dimensional subalgebras of Diff2. As an application, we classify the symmetries of second order equations.