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Preface CHAPTER I General Concepts and Notations 1 Spaces and Mappings
Fiber Mappings and Vector Bundles
Transformation Groups Intertwining Maps and Linear Group Actions on Vector Bundles
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action assigning associated associative algebra base basis bilinear calculate called Chapter commutation condition connected Consider consists construct coordinates course cross-sections defined DEFINITION denoted derivatives described determined differ differential operator direct dual element equations equivalence Euler-Lagrange example Exercise exists fact fiber space follows formula functions further geometric given gives hence Hermitian homomorphism ideas identified identity implies inner product interesting invariant irreducible isomorphism Lagrangian Lie algebra Lie group linear connection linear transformation Lorentz manifold mathematical means module notation Notice orbits particular physical Poincaré preserves problem projection Proof prove quantum field theory quantum mechanics quotient reader readily real numbers Recall relation representation respect result right hand side satisfying Show structure subgroup subset Suppose symmetric tensor THEOREM turn unitary variations vector bundle vector space