The Mathematical Foundations of Gauge TheoriesTheoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism. |
Common terms and phrases
4-manifold A¹(M ad(P adjoint base manifold bosons called canonical chain complex characteristic classes Chern class classical Clifford algebras cohomology compact corresponding curvature defined definition denote diffeomorphism differential manifold dimension discussion electroweak element example exists fiber bundle field equations finite dimensional function fundamental gauge connection gauge field gauge group gauge potential gauge theories gauge transformations geometry given GL(n gravitational group G Higgs homology homomorphism homotopy groups induces inner product instanton number integral intersection form isomorphism Lagrangian Lie algebra Lie group linear Math mathematical metric moduli space morphism obtained oriented P-module particle Phys physical polynomial principal bundle quantization quantum field theory quaternionic resp Riemannian manifold satisfies self-dual singular smooth solutions spin spinor structure group subgroup subset symmetric tion topological space vector bundle vector field vector space Yang-Mills action Yang-Mills equations Yang-Mills fields Yang-Mills-Higgs