A new role for the vector potential in quantum theory.
The thesis begins with a discussion of causality
as used in Physics. It distinguishes between two kinds
of causes, the efficient and the formal, and argues that
though the latter has always existed in Physics, it has
remained mainly on the tacit level. It goes on to point
out that the formal cause is of particular importance to
quantum mechanics and unless it is introduced explicitly
and on the same footing as the efficient cause, paradoxical
and intuitively unintelligible results are likely to
Indeed, one such result is the Aharonov-Bohm effect
where the vector potential seems to play an ambiguous role.
The second chapter examines some of the attempts to explain
this effect and comes to the conclusion that it cannot be
done by forcing the problem into the existing formalism.
Rather, a more radical approach is needed based on the
Chapter three takes a closer look at the effect with
a view to understanding more clearly its structural features,
a necessary preparation for the introduction of the formal
Chapter four examines cases whose forms are analogous
to that of the Aharonov-Bohm effect in order to gain some
insight into the features which might be used for a
structural reformulation of that effect.
Finally, chapter five attempts a mathematical approach
based on the formal cause. This is first applied to the
classical cases of a particle inside and outside an electromagnetic
field where use is made of global referentiframes. The Aharonov-Bohm effect is then treated by
replacing the referential frames by the quantum potential.
The structural features of the latter are examined in
detail with the help of computer generated three-dimensional
plots. These results predict clearly visualisable changes
of symmetry, brought about by the vector potential, which
affect the distributions of well defined particle trajectories.
The chapter is concluded with a brief outline of other
applications of the structural approach