Non commutative geometry and physics
GEOMETRIE NON COMMUTATIVE
C*-ALGEBRES
TOPOLOGIE
COHOMOLOGIE
THEORIE QUANTIQUE
FIBRES VECTORIELS
PHYSIQUE MATHEMATIQUE
CONNES
M/93/32
IHES
06/1993
A4
70 f.
EN
TEXTE
PREPUBLICATION
M_93_32.pdf
1993
Symmetry and classification of energy bands in crystals
SOLIDES
CLASSIFICATION
ENERGIE
GROUPES SPATIAUX
To appear in Proceedings XVth International Colloquium on Group Theretical Methods in Physics (Varna, June 1987)
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.
MICHEL
BACRY
ZAK
P/87/42
IHES
10/1987
A4
11 f.
EN
TEXTE
PREPUBLICATION
P_87_42.pdf
1987
Structure and classification of band representations
CRISTALLOGRAPHIE
SOLIDES
ASTRONOMIE
ORBITE
ETOILES
MODELISATION
ENERGIE
ATOMES
Abstract : Band representaitons in solids are investigated in the general framework of induced representations by using the concepts of orbits (stars) and strata (Wyckoff positions) in their construction and classification. The connection between band representations and irreducible representations of space groups is established by reducing the former in the basis of quasi-Bloch functions wich are eigenfunctions of translations but ar not, in general, eigenfunctions of the Hamiltonian. While irreducible representations of space group ar fnite-dimensional and are induced from infinite-order little groups Gk for vectors K in the Brillouin zone, band representations are infinite-dimensional adn are induced from finite-order little groups Gr for vectors r in the Wigner-Seitz cell. This connection between irreductible representations and band representations of space groups shedd new light on the duality properties of the Brillouin zone and the Wigner-Seitz cell. As an introduction to band representations the induced representations of point groups wich id applied to the investigation of th equivalency of band representations. Based on this connection and on the properties of the crystallographic point groups a necessary condition id established for the inequivalency of band representations induced from maximal isotropy groups. For using this condition there is need fro the induced representaitons of oint groups and a full list of them is given in the paper. One is especially interested in irreducible-band representations which form the elementary building bricks for band representations. From the point of view of the physics, irreducible-band representations correspond to energy bands with minimal numbers of branches. A method id developped for finding all the inequivalent irreducible-band representations of space groups by using the induction from maximal isotropy groups. As a rule the latter leads to inequivalent irreducible-band representations. There are, however, few exceptions to this rule. A full list of such exceptions is tabulated in the paper. With this list at hand one can construct all the different irreducible-band representations of 2-dimensional space groups. For them we list the continuity chords of all their irreducible-band representations.
MICHEL
BACRY
ZAK
P/86/35
IHES
06/1986
A4
46 f.
EN
TEXTE
PREPUBLICATION
P_86_35.pdf
1986
What is a Crystal ?
CRISTAUX
MATHEMATIQUES
PAVAGE
FONCTIONS
Abstract : An historical survey of our knowledge of crystal structure and of the mathematical problem of paving space with one or a few types of stones show that a crystal has not necessarily a translation lattice. The recently discovered crystals of alloys Al with 14% Mn have an ecosahedral symetry (incompatible qith translation lattice). Their electron micrographs show a structure similar to a Penrose tiling. It seems that long range order characterizing crystals can be obtained from projection of a thin slab of genuine crystal in higher dimension so that crystal physical properties can be described by quasi-periodic functions (as generalizing periodic ones) or may be almost periodic functions.
MICHEL
P/85/68
IHES
12/1985
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_85_68.pdf
1985
Some Use of metabelian groups in physics
THEORIE DES GROUPES
GROUPES RESOLUBLES
CLASSIFICATION
Abstract : Metabelian groups are those whose structure differ the least from Abelian groups. We explain the classification of finite metabelian groups and give some examples of physics problems where they play an important role.
MICHEL
MOZRZYMAS
P/83/20
IHES
03/1983
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_83_20.pdf
1983
The Structure of unitary representations of space groups
GROUPES SPATIAUX
REPRESENTATIONS DE GROUPES
CRISTALLOGRAPHIE
Lecture given by L. Michel at the XI-th International colloquium on Group Theoretical Methods in Physics at Istanbul, August 1982
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.
MICHEL
MOZRZYMAS
P/82/54
IHES
10/1982
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_82_54.pdf
1982
Représentation de vibration d'un cristal construite par induction de représentations
CRISTALLOGRAPHIE
MATHEMATIQUES
VIBRATIONS
ANALYSE VECTORIELLE
Résumé : La représentation du groupe d'espcace GK d'un vecteur d'onde k est le produit tensoriel de la représentation vectorielle du groupe ponctuel Pk de k et d'une représentation induite donnée explicitement.
L'utilisation du théorème de réciprocité de Frobenius simplifie l'étude de la décomposition de la représentation de vibration de Gk en somme directe de représentations irréductibles.
MICHEL
MOZRZYMAS
P/82/33
IHES
06/1982
A4
4 f.
FR
TEXTE
PREPUBLICATION
P_82_33.pdf
1982
Symmetry in condensed matter physics
SYMETRIE
MATIERE CONDENSEE
MICHEL
P/81/58
IHES
11/1981
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_81_58.pdf
1981
The Description of the symmetry of physical states and spontaneous symmetry breaking
SYMETRIE
SYMETRIE BRISEE
MATIERE CONDENSEE
Lecture given on September 1st, 1980 at the Colloque Pierre Curie sur La Symetrie et les ruptures de sypétrie en phyisque de la matière condensée
MICHEL
P/80/37
IHES
10/1980
A4
9 f.
EN
FR
TEXTE
PREPUBLICATION
P_80_37.pdf
1980
Symmetry and topology of energy bands in crystals
CRISTAUX
BANDES D'ENERGIES
SYMETRIE
TOPOLOGIE
Lecture given at the internation schoolon Symmetry abd Structural Properties of Condensed Matter. August 27 - September 2, 1998, Zajaczkowo (Posnan), Poland.
MICHEL
P/99/07
IHES
01/1999
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_99_07.pdf
1999
Recent results on the implications of crystal symmetry and time reversal
ZONES DE BRILLOUIN
COMPACTIFICATIONS
CRISTAUX
POLYNOMES
SYMETRIE
ANALYSE NUMERIQUE
Lecture given on August 1rst 1997 at the VIIIth International Conference on Symmetry Methods un Physics. JINR, Dubna, Russia.
MICHEL
P/98/09
IHES
02/1998
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_98_09.pdf
1998
Wigner memorial lecture
CONGRES ET CONFERENCES
WIGNER
MELANGES ET HOMMAGES
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
MICHEL
P/96/81
IHES
12/1996
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_96_81.pdf
1996
Physical implications of crystal symmetry and time reversal
RESEAUX CRISTALLINS
SYMETRIE
ESPACE ET TEMPS
Lectures given at the international school on Symmetry and Structural Properties of Condensed Matter. August 28 - September 5, 1996, Zajaczkowo (Posnan), Poland.
MICHEL
P/96/80
IHES
12/1996
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_96_80.pdf
1996
Extrema of P-invariant functions on the Brillouin zone
ZONES DE BRILLOUIN
THEORIE DE MORSE
MAXIMUMS ET MINIMUMS
CRISTALLOGRAPHIE
MATHEMATIQUES
SYMETRIE
PHYSIQUE
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.
MICHEL
P/92/16
IHES
04/1992
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_92_16.pdf
1992
On the statistical mechanics of classical Coulomb - and dipole gases
MECANIQUE STATISTIQUE
GAZ
PHYSIQUE NUCLEAIRE
FROHLICH
SPENCER
P/80/10
IHES
1980
A4
65 f.
EN
TEXTE
PREPUBLICATION
P_80_10.pdf
1980
Levi-Civita and the general relativistic problem of motion
LEVI-CIVITA
RELATIVITE GENERALE
MECANIQUE ANALYTIQUE
MOUVEMENT
DAMOUR
SCHAFER
P/90/60
IHES
07/1990
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_90_60.pdf
1990