Kinematic Quantum Geometry

arXiv:2611.13089v1 Announce Type: new Abstract: Kinematic quantum geometry describes fast degrees of freedom (DOFs) that adiabatically follow states parametrized by both the coordinates and the velocities of slow DOFs. It extends Born-Oppenheimer geometry, which depends on coordinates alone, introduces mixed Berry curvatures, and modifies the effective theory governing the slow DOFs. We test its predictions in two setups: spinful particles moving in magnetic textures, and Dirac electrons in graphene coupled to an LC circuit. In the first, kinematic quantum geometry produces a velocity-dependent effective mass tensor and generates a Lorentz-like force nonlinear in velocity that can arise even in coplanar textures.