Direct Observation of the Particle Exchange Geometric Dynamic Phase of Polarized Fermions
Subhamoy Singha Roy
Department of Physics, JIS College of Engineering, Kalyani, India
Abstract: Given this, it is found that the exchange phase for polarized fermions is provided by the Berry phase. In the case of noncontractible loops in a nonsimply connected space, the exchange phase lacks curvature and is associated with the first Stiefel-Whitney class of the two spin bundle. In contrast, the Chern class—where the Chern number is determined by the integral of the curvature—is linked to the Berry phase, which is the holonomy element of the connection. The exchange phase for polarized fermions is determined by the Berry phase. This is because the -symmetry breakdown in this scenario means that the Stiefel-Whitney class, which is significant in the -cohomology, is not applicable. Because of this, the exchange phase for chiral fermions may be realized as the well-known Berry phase.