DIRAC MAGNETIC MONOPOLE AND THE AHARONOV-BOHM SOLENOID IN THE POINCARE GAUGE

The author considers the Poincare (or multipolar) gauge with finite and infinite reference point in connection with singularities of the Aharonov-Bohm solenoid and Dirac magnetic monopole type. Families of paths on which the Poincare gauge potentials are defined may give rise to 'shadow' surface or regions on which the Poincare gauge potentials are singular. These singularities may be avoided by changing the family of paths to another family (based on the same reference point) and this is equivalent to changing the gauge. He considers the Dirac magnetic monopole using the Poincare gauge with a family of parallel straight paths from reference points situated at (0,0,0,+or- infinity ), producing the 'overlapping' potentials for the monopole. A method is given for calculating the Poincare gauge potentials on the shadow surface arising from a singularity, and this is illustrated by considering the solenoid problem in which the solenoid is given a finite radius ( in ), and it is shown that the shadow surface in this case contains singularities of the Dirac delta function type.