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REVIEW OF THE THEORY OF FIELD LAGRANGIANS
Lagrangians Cartan Forms and Symmetries
Lagrangians Invariant Under a Given
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1-forms affine connection affine maps automorphisms base-like bilinear form called Cartan structure change in parameterization Chapter classical conformal connection defined connection for T(N connection forms coordinate system cosymplectic covariant derivative cross-sections curvature forms curvature tensor Definition denote DGCV differential equations dimension Dirac equation dual Ehresmann connection element Exercise following condition following form functions geodesic geometric grad f Hamiltonian Hence homomorphism infinitesimal integral curves isomorphism Lagrangian Lie algebra Lie group linear connection linear map mathematical matrix moving frame notations open subset parallel translation parallel transport particle Pfaffian system physics Poisson bracket projective connection Proof Prove real numbers relation Remark Riemannian manifolds Riemannian metric right hand side Section Show skew-symmetric spin spinorial straight line structure group Suppose symmetric symplectic structure tangent bundle tangent vector tensor product Theorem 6.1 theory variables Vd A Vd vector bundle vector field system vector space Weyl Weyl-Cartan property