The Aharonov-Bohm Effect

Faraday and Maxwell introduced the concept of the electromagnetic field to describe electromagnetic effects in a space-time region -thereby unifying electrical and magnetic phenomena.The field strength Ff. describes electromagnetism.In 1959 Bohm and Aharonov presented a paper In which they pointed out the signi ficance of electromagnetic potentials in quantum theory and actually suggested.Interference experiments to detect how potentials would affect the passage of electrons through field free regions.In a multiply connected, region even if F^= o everywhere, there are physical experiments for which the outcome depends on the loop integral: he OA^dx'^ around on unshrinkable loop.It has been realised that in fact only the phose factor exp ( i0 A ,d x e ) in meaningful and phase invariance (gauge invariance) is the correct quantum mechanical, characterisation of electromagnetism.The idea has in recent years been generalised by replacing the simple phase of complex numbers with more complicated phase-an element of a Lie group.Few effects in physics have the distinctions of going through extensive debates and experimentations to settle the nuances as in AB effect.The contro versial aspects of AB effect concern mainly its interpretation.To quote Bohm "N ow in my view, the fact that our informal discussion of interaction in terms of forces has been shown to be irrevalent implies the need, for a new kind of informal discussion of this question.That is what I meant by saying that AB effect indicates the need to alter our informal terms of discussion of the vector potential as having a new kind of significance".This was expressed in a communication to one of the authors (M P) of the book under review.There is not much disagreement today as to the effect itself-well verified through delicate and precise measurements in which the state of the art has attained, astounding precision.However, questions concerning localisation and action at a distance remain alive.So, it is in this backdrop that "The Aharonov-Bohm Effect" by M Peshkin and A Tonomura has to be examined.The book consists of two parts.The