Anticipations of the Geometric Phase

In science we like to emphasize the novelty and originality of our ideas. This is harmless enough, provided it does not blind us to the fact that concepts rarely arise out of nowhere. There is always a historical context, in which isolated precursors of the idea have already appeared. What we call "discovery" sometimes looks, in retrospect, more like emergence into the air from subterranean intellectual currents. The geometric phase, whose discovery I reported early in 1983, is no exception to this rule. The paper was about quantum systems forced round a cycle by a slow circuit of parameters that govern them; it gave rise to a number of applications and several generalizations, documented in a series of reviews and books." My purpose here is to look back at some early studies that with hindsight we see as particular examples of the geometric phase or the central idea underlying it.