Group Structure of Gauge Theories
This monograph provides an account of the structure of gauge theories from a group theoretical point of view. The first part of the text is devoted to a review of those aspects of compact Lie groups (the Lie algebras, the representation theory, and the global structure) which are necessary for the application of group theory to the physics of particles and fields. The second part describes the way in which compact Lie groups are used to construct gauge theories. Models that describe the known fundamental interactions and the proposed unification of these interactions (grand unified theories) are considered in some detail. The book concludes with an up to date description of the group structure of spontaneous symmetry breakdown, which plays a vital role in these interactions. This book will be of interest to graduate students and to researchers in theoretical physics and applied mathematics, especially those interested in the applications of differential geometry and group theory in physics.
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Global properties of groups and Lie groups
Local properties of Lie groups
Hermitian irreducible representations of compact simple Lie algebras
Continuous unitary irreducible representations CUIRs of compact Lie groups
Rigid internal groups
The gauge principle
Spontaneous symmetry breaking
abelian adjoint representation antisymmetric assignments asymptotic freedom baryons Cartan algebra Casimir coefficients colour commutation compact groups compact Lie groups compact simple Lie components condition conjugation cosets coupling constant CUIRs defined diagonal dimensional Dynkin eigenvalues electroweak elements equation Euclidean example fermion finite fundamental representation gauge fields gauge theory Goldstone fields grand unification group G hadrons hence Higgs mechanism highest weight HIRs homomorphism inner product integer invariant with respect irreducible representations Lagrangian leptons linear massless maximal little groups mesons multiplication law Noether charges Nucl orbits orthogonal parameters Phys physical potential primitive representations primitive roots problem properties quantum numbers quarks quotient group renormalizable representation of SU(n result satisfy scalar fields semi-simple simple groups singlet SO(n spinor representations spontaneous symmetry breaking strong interactions structure constants SU(n subalgebra symmetry breakdown symmetry group tensor representations topology transformations true groups unitary vector Weyl zero