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Group theory : application to the physics of condensed matter / M S Dresselhaus, G Dresselhaus, A Jorio
Berlin : pringer-Verlag, 2008
582 p.
Ký hiệu phân loại (DDC): 530.1522
"Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra, this concise and class-tested-book has been pedagogically tailored over 30 years at MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn; understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours)." "From there, each: chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented. Essential problem sets between the chapters also aid the retention of the new material and for the consolidation of material learned in previous chapters. The text and problem sets have proved a, useful springboard for the application of the basic material presented here to topics in semiconductor physics and the physics of carbon-based nanostructures."
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Group theory applied to chemistry / Arnout Ceulemans
Dordrecht : Springer, 2013
269 p.
Ký hiệu phân loại (DDC): 541.2
Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons. This textbook introduces the subtle metaphors which relate our macroscopic understanding of symmetry to the molecular world. It gradually explains how bodily rotations and reflections, which leave all inter-particle distances unaltered, affect the study of molecular phenomena that depend only on these internal distances. It helps readers to acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research.
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Introduction to Λ-trees / Ian Chiswell
Singapore ; River Edge, N.J : World Scientific, 2001
315 p. : illustrations ; 22 cm.
Ký hiệu phân loại (DDC): 511.52
"The theory of [lambda]-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of [lambda]-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmüller space for a finitely generated group using R-trees. In that work they were led to define the idea of a [lambda]-tree, where [lambda] is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on R-trees, notably Rips' theorem on free actions. There has also been some progress for certain other ordered abelian groups [lambda], including some interesting connections with model theory. Introduction to [lambda]-Trees will prove to be useful for mathematicians and research students in algebra and topology."
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