not view fields as sections but simply as functions . In other words, vector bundles at different points are comparable. In addition, for flat spacetime the Levi-Civita connection is the trivial connection on the frame bundle. Then the spacetime covariant derivative on tensor or spin-tensor fields is simply the partial derivative in flat coordinates. However the gauge covariant derivative may require a non-trivial connection which is considered to be the gauge field of the theory. Accuracy as a physical model In weak gravitational curvature, flat spacetime often serves as a good approximation to weakly curved spacetime. For experiment, this approximation is good. The Standard Model is defined on flat spacetime, and has produced the most accurate precision tests of physics to date. See also Classical field theory Exterior algebra Lagrangian system Variational bicomplex Quantum field theory Non-autonomous mechanics Higgs field (classical) References Saunders, D.J., "The Geometry of Jet Bundles", Cambridge University Press, 1989, Bocharov, A.V. [et al.] "Symmetries and conservation laws for differential equations of mathematical physics", Amer. Math. Soc., Providence, RI, 1999, De Leon, M., Rodrigues, P.R., "Generalized Classical Mechanics and Field Theory", Elsevier Science Publishing, 1985, Griffiths, P.A., "Exterior Differential Systems and the Calculus of Variations", Boston: Birkhäuser, 1983, Gotay, M.J., Isenberg, J., Marsden, J.E., Montgomery R., Momentum Maps and Classical Fields Part I: Covariant Field Theory, November 2003 Echeverria-Enriquez, A., Munoz-Lecanda, M.C., Roman-Roy, M., Geometry of Lagrangian First-order Classical Field Theories, May 1995 Giachetta, G., Mangiarotti, L., Sardanashvily, G., "Advanced Classical Field Theory", World Scientific, 2009, () Differential topology Differential equations Fiber bundles Theoretical physics Lagrangian mechanics