5 research outputs found
The Landau electron problem on a cylinder
We consider the quantum mechanics of an electron confined to move on an
infinite cylinder in the presence of a uniform radial magnetic field. This
problem is in certain ways very similar to the corresponding problem on the
infinite plane. Unlike the plane however, the group of symmetries of the
magnetic field, namely, rotations about the axis and the axial translations, is
{\em not} realized by the quantum electron but only a subgroup comprising
rotations and discrete translations along the axial direction, is. The basic
step size of discrete translations is such that the flux through the `unit
cylinder cell' is quantized in units of the flux quantum. The result is derived
in two different ways: using the condition of projective realization of
symmetry groups and using the more familiar approach of determining the
symmetries of a given Hamiltonian.Comment: 26 pages, revtex file, no figures. In version 2, introduction is
expanded to explain our approach and references are updated. Results and
conclusions are unchange
Family Unification from Universality
A direct consequence of the occurrence of fermion families is the invariance
of currents under certain groups of (universality) transformations. We show how
these universality groups can themselves be used to find and study grand family
unification models. Identifying two independent - weak and strong -
universality groups and assuming that the grand unification group is SU(8N),
its subgroup respecting either weak or strong universality is shown to be G =
SU(2)xU(1)xSU(3). The fundamental representation of SU(8N) decomposes as N
families of leptons and quarks. In the G-invariant limit, all fermions are
left-handed. A mechanism for generating the correct number of right-handed
fermions with the correct couplings so as to give pure vector colour and
electromagnetic currents is exhibited. Universality is shown to result most
naturally from a preonic structure of fermions. In such a preonic picture there
are no ultraheavy gauge bosons and no anomaly or hierarchy problem.Comment: 30 page