Geometry of the standard model of elementary particles
The book deals with the standard model of elementary particles. The exposition emphasizes the naturally geometric character of particle theories. Particles and their interactions are described in terms of vector bundles over spacetime and operations on them. The approach differs from the existing literature by very consistent use of the geometric language. No previous knowledge of physics is assumed. The book can be used by both pure and applied mathematicians including graduate students of mathematics, to quickly learn the basics of particle physics. To physics students, this book offers a brief survey of the central topics in classical particle theory, based on a coordinate-free geometric formulation.
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Particles and Vector Bundles
Invariants of Particles
More on Relativistic Particle Models
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3-space affine bundle angular momentum antiparticle antiquarks baryons bosons bundle 77 characterized charge q complex vector bundle conjugate consists constant corresponding decomposition defined described Dirac spinor Dirac spinor bundle direct sum electric charge electromagnetic interaction electromagnetism bundle electron electroweak model equivalence Euclidean Example fact fermions fibre dimension field equations fixed function G-structure geometry hadrons Hermitian fibre metric homomorphism inner product interacting-particle bundle interaction bundle interaction carriers invariant irreducible representation isospin Klein-Gordon equation Lagrangian Leite Lopes 1981 leptons Lie algebra line bundle Lorentz mass massless matter particles mesons Minkowski spacetime morphism multiplet multiplication natural bundle natural isomorphism neutrino notation obtained obviously orientation orthogonal parity particle species photon physical quantization quantum numbers quark content quark flavors References relativistic Remark replaced represented Ryder sections ip so(V spinor bundle strong interaction structure group SU(n subbundle subspace Sudbery symmetry breaking tensor product unique vacuum values vector space Weyl Yang-Mills