Group Theory and PhysicsCambridge University Press, 1995 M09 7 - 429 pages This book is an introduction to group theory and its application to physics. The author considers the physical applications and develops mathematical theory in a presentation that is unusually cohesive and well-motivated. The book discusses many modern topics including molecular vibrations, homogeneous vector bundles, compact groups and Lie groups, and there is much discussion of the group SU(n) and its representations, which is of great significance in elementary particle physics. The author also considers applications to solid-state physics. This is an essential resource for senior undergraduates and researchers in physics and applied mathematics. |
Contents
Basic definitions and examples | 1 |
Representation theory of finite groups | 48 |
Molecular vibrations and homogeneous vector bundles | 94 |
Compact groups and Lie groups | 172 |
The irreducible representations of SUn | 246 |
classes | 309 |
symmetric group | 327 |
symmetries | 354 |
groups | 407 |
Further reading | 424 |
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Common terms and phrases
action of G atom axis basis character table coefficients compact support compute conjugacy class consider consists corresponding crystal decomposes decomposition define density determined diagonal dimensional direct sum eigenvalue eigenvector electron elements energy entries equation example F₁ finite finite-dimensional formula function G acts G x G G₂ given gives group G hence Hilbert space identity integer interaction invariant subspace irreducible representations isomorphic isotropy group lattice lemma Lie algebra linear combinations linear transformation lines M₁ matrix molecule multiplication obtain one-dimensional operator orbit orthogonal particles permutation plane Poincaré group prove quantum mechanics quarks representation of G rotation satisfying scalar product Schur's lemma smooth spanned spectra spectrum spin subgroup Suppose symmetry group tabloid tensor product theorem theory trivial unitary V₁ V₂ values vector bundle vector space W₁ weight vector write Young diagram zero