A unified view of curvature and torsion in metric–affine gauge theory of gravity through affine–vector bundles

One of the most appealing results metric-affine gauge theory gravity is a close parallel between Riemann curvature two-form and Cartan torsion two-form: While former field strength Lorentz-group connection one-form, latter can be understood as coframe one-form. This parallel, unfortunately, not fully established until one adopts Trautman's idea introducing an affine-vector-valued zero-from, meaning which has been satisfactorily clarified. paper aims to derive this from first principles without any ad hoc prescriptions. We propose new mathematical framework associated affine-vector bundle more suitable arena for affine group than conventional vector bundle, rigorously covariant derivative local section on in formal Ehresmann-connection approach. The arises naturally their geometric physical meanings become transparent. clear picture also leads conjecture about kinematical effect that principle measured \`{a} la Aharonov-Bohm effect.