FTP, name the electromagnetic vector field that is often symbolized A and the curl of which is equal to the magnetic field.
The Aharonov-Bohm effect is the classically impossible influence of this field alone upon charged particles, and it is introduced along with its counterpart to collapse a set of four PDE's to a set of two.  The square of the norm of its combination with its scalar counterpart is Lorentz invariant, and its relation to the vector field it generates is suggested by Gauss' law for that field, since the divergence of the curl of a well-behaved vector field identically vanishes.  It may be transformed by the addition of the gradient of a scalar gauge function.  FTP, name the electromagnetic vector field that is often symbolized A and the curl of which is equal to the magnetic field.
The Aharonov-Bohm effect is the classically impossible influence of this field alone upon charged particles, and it is introduced along with its counterpart to collapse a set of four PDE's to a set of two.  
magnetic vector potential (prompt on "A" or "potential")