Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations. .

Physics. --- Topological groups. --- Lie groups. --- Mathematical physics. --- Nuclear physics. --- Mathematical Methods in Physics. --- Mathematical Physics. --- Particle and Nuclear Physics. --- Topological Groups, Lie Groups. --- Topological Groups. --- Physical mathematics --- Physics --- Groups, Topological --- Continuous groups --- Mathematics --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Symmetry (Physics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: “This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.” — The Mathematical Gazette.

Mathematics. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Algebra. --- Topological Groups. --- Cell aggregation --- Mathématiques --- Algèbre --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Manifolds (Mathematics). --- Complex manifolds. --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Representations of Lie groups. --- Representations of Lie algebras. --- Lie algebras. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Lie groups --- Representations of Lie algebras --- Representations of Lie groups --- Cell aggregation_xMathematics --- Topological Groups --- Complex manifolds --- Nonassociative rings --- Electronic books

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Topological groups. Lie groups --- 512.812 --- Lie groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- General Lie group theory. Properties, structure, generalizations. Lie groups and Lie algebras --- Lie groups. --- 512.812 General Lie group theory. Properties, structure, generalizations. Lie groups and Lie algebras

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge­ bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan­ dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

Kac-Moody algebras. --- Representations of groups. --- Flag manifolds. --- Kac-Moody, Algèbres de --- Représentations de groupes --- Variétés de drapeaux (Géométrie) --- Representations of groups --- Flag manifolds --- Kac-Moody algebras --- Kac-Moody, Algèbres de --- Représentations de groupes --- Variétés de drapeaux (Géométrie) --- Algebraic topology. --- Topological groups. --- Lie groups. --- Algebra. --- Algebraic geometry. --- Group theory. --- Algebraic Topology. --- Topological Groups, Lie Groups. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic geometry --- Geometry --- Mathematics --- Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Topology

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Topological groups. Lie groups --- Lie groups. --- Lie algebras. --- Groupes de Lie --- Algèbres de Lie --- Algèbres de Lie --- 512.81 --- 512.81 Lie groups --- Lie groups --- Lie, Algèbres de --- Lie, Groupes de