In the case of cylindrical symmetry for an electron gas the effective
physics is 2D in the r,theta plane perpendicular to the z-axis of
symmetry. That is, the physics should not depend on z in that case. An
external magnetic field is along z and that provided magnetic flux to
attach to the electrons to make anyons with fractional effective angular
momenta, charges and weird quantum statistics neither fermion nor boson
for general @.
That is
cc* + e^i@c*c = 1
@ ~ magnetic field
Note "effective" statistically averaged charges and angular momenta do
not necessarily imply that the individual systems have fractional
charges in the case of entangled states
|anyon>
~ |free electron>A|magnetic flux>A + |bound electron>B|magnetic flux>B
for the composite anyon
.
|
