Dimensional reduction of gauge theories, spontaneous compactification and model building
This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included and they review attempts to construct realistic models. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.
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Dimensional reduction of pure YangMills theories
Dimensional reduction of gravity and spontaneous
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adjoint representation assumption automorphisms calculate canonical characterizing components connection form constraint equation corresponding cosmological constant curvature form Decomposing decomposition defined denote dimensional reduction dimensional reduction method discussed Einstein-Yang-Mills system equations of spontaneous equivariant mapping fibre bundle field equations four dimensions fulfilling G-invariant metric G-symmetric G/H being symmetric gauge group gauge potential Gauge Theories geometrical given gravity Higgs potential homomorphism irreducible representations K-bundle Lagrangian Lie algebra Lie group mass massless model building Moreover multidimensional theory multidimensional universe Neutrino non-trivial obtain orthonormal frames parameters particles physical principal bundle problem Proceedings pure Yang-Mills theories quantum reduced action reduced gauge group reduced theory respect restrict ourselves scalar curvature scalar field scalar field potential scalar product solutions solve spinor field spontaneous compactification spontaneous symmetry breaking structure group subbundle subsection subspace tion torsion trivial representation values vol(K volume form Yang-Mills field Yang-Mills theories