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Effective dynamics for a spin-1/2 particle constrained to a space curve in an electric and magnetic field

We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics and derive the effective Hamiltonian. A new type of quantum potential called SU(2) Zeeman interaction appears, which is induced by the electric field and couples spin and intrinsic orbital angular momentum. Based on the Hamiltonian, we discuss the spin precession for zero intrinsic orbital angular momentum case and the energy splitting caused by the SU(2) Zeeman interaction for a helix as examples, showing the combined effect of geometry and external field. The new interaction may bring new approaches to manipulate quantum states in spintronics.