Berry connection and curvature

In physics, Berry connection and Berry curvature are related concepts which can be viewed, respectively, as a local gauge potential and gauge field associated with the Berry phase or geometric phase. The concept was first introduced by S. Pancharatnam^[1] as geometric phase and later elaborately explained and popularized by Michael Berry in a paper published in 1984^[2] emphasizing how geometric phases provide a powerful unifying concept in several branches of classical and quantum physics.