"This book is a collection of lecture notes which were presented by invited speakers at the Eleventh School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter SSPCM 2014" in Rzeszów (Poland) in September 2014. The main challenge for the lecturers was the objective to present their subject as a review as well as in the form of introduction for beginners. Topics considered in the volume concentrate on: spin dynamics and spin transport in magnetic and non-magnetic structures, spin-orbit interaction in two-dimensional systems and graphene, and new mathematical method used in the condensed matter physics."--
This book is a collection of lecture notes which were presented by invited speakers at the Eleventh School on Theoretical Physics 'Symmetry and Structural Properties of Condensed Matter SSPCM 2014' in Rzeszów (Poland) in September 2014. The main challenge for the lecturers was the objective to present their subject as a review as well as in the form of introduction for beginners. Topics considered in the volume concentrate on: spin dynamics and spin transport in magnetic and non-magnetic structures, spin-orbit interaction in two-dimensional systems and graphene, and new mathematical method used in the condensed matter physics.
The aIm of the present article is to give a critical exposition of the theory of the symmetry properties of rigid and nonrigid molecules. Despite the fact that several accounts of the subject, both technical and didactic, are now available, and despite the extensive discussion of nonrigid molecule symmetry that has been going on since the classic papers of Hougen and Longuet-Higgins, there remains a need for a unifying survey of the problem. Previous treatments have tended to emphasize one or the other particular viewpoint at the expense of a broader view. Renewed interest in the details of the symmetry classification of rotation vibration states of highly symmetric (octahedral) molecules has led to a reexam ination of the relation between conventional point group operations and permutations of identical nuclei in rigid molecules, together with a clarification of the fundamental role of the Eckart constraints and associated Eckart frame. As is shown below, analogous insights can also be obtained in the case of nonrigid molecule symmetry, where the Eckart-Sayvetz conditions provide a natural generalization of the Eckart constraints. The importance of particular definitions of the 'molecule-fixed' frame in the theory of molecular symmetry can be better appreciated by examining their dynamical origin. Chapter 1 is therefore devoted to a description of the derivation of the usual Wilson-Howard-Watson form of the molecular Hamiltonian, together with its generalization to nonrigid molecules. Particular attention is given to the intro duction of molecular models and use of the Eckart and Eckart-Sayvetz constraints.
These notes essentially reproduce lectures given at the International School for Advances Studies (Trieste) and at the Scuola Normale Superiore (Pisa) on various occasions. The scope of the short series of lectures was to extend on general grounds, also to mathematicians, the phenomenon of Spontaneous Symmetry Breaking (SSB), a mechanism which seems at the basis of the recent developments in theoretical physics (from statistical mechanics to many-body theory and to elementary particle theory). Besides its extraordinary success, the idea of SSB deserves being discussed also because of its innovative philosophical content and in our opinion it should be part of the background knowledge for mathematical and theoretical physics students, especially those who are interested in questions of principle and in general mathematical structures.
This lecture note provides a tutorial review of non-Abelian discrete groups and presents applications to particle physics where discrete symmetries constitute an important principle for model building. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics—particularly model building beyond the standard model—non-Abelian discrete symmetries have been applied particularly to understand the three-generation flavor structure. The non-Abelian discrete symmetries are indeed considered to be the most attractive choice for a flavor sector: Model builders have tried to derive experimental values of quark and lepton masses, mixing angles and CP phases on the assumption of non-Abelian discrete flavor symmetries of quarks and leptons, yet lepton mixing has already been intensively discussed in this context as well. Possible origins of the non-Abelian discrete symmetry for flavors are another topic of interest, as they can arise from an underlying theory, e.g., the string theory or compactification via orbifolding as geometrical symmetries such as modular symmetries, thereby providing a possible bridge between the underlying theory and corresponding low-energy sector of particle physics. The book offers explicit introduction to the group theoretical aspects of many concrete groups, and readers learn how to derive conjugacy classes, characters, representations, tensor products, and automorphisms for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest. Further, CP symmetry and modular symmetry are also presented.
These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand the three-generation flavor structure in particular. Indeed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark and lepton masses, and mixing angles by assuming non-Abelian discrete flavor symmetries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abelian discrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory - e.g. the string theory or compactification via orbifolding – thereby providing a possible bridge between the underlying theory and the corresponding low-energy sector of particle physics. This text explicitly introduces and studies the group-theoretical aspects of many concrete groups and shows how to derive conjugacy classes, characters, representations, and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest.
Imparts a deeper understanding of symmetry principles applied to atomic and molecular dynamics and spectroscopy. Exposes the most powerful mathematical methods without sacrificing physical comprehension. Contains a thorough treatment of group representation theory and applications using projection algebra and subgroup chains. Features extensive graphics and visual aids for wave mechanics and operator algebra.
