Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivation of the Aharanov Bohm phase shift using classical forces   In 1959 Aharonov and Bohm suggested that an electron passing around a long
solenoid would pick up a phase shift dependent on the magnetic field of the
solenoid, even though the electrons themselves pass through a region of space
which has a zero magnetic field. It has long been held that this result is
purely quantum and is derived in many well known quantum mechanics text books
using the Schrodinger equation and vector potential. Here the same phase shift
is derived from a purely classical force, but relativistic transformations are
taken into account. The force is in the direction of motion of the electron (or
opposite) leading to a phase advance (or lag) and we obtain precisely the phase
shift thought previously to be purely quantum. The only quantum result used
here is the de Broglie wavelength of the particle, in order to get two slit
like interference and the phase shift. We employ a stack of dipoles as the
solenoid and note the same force on the electron in two different frames of
reference. We shall consider the solenoid stationary and the electron moving,
and then consider the electron rest frame and consider the solenoid moving in
the opposite direction.

28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an