173 research outputs found
Dual families of non-commutative quantum systems
We demonstrate how a one parameter family of interacting non-commuting
Hamiltonians, which are physically equivalent, can be constructed in
non-commutative quantum mechanics. This construction is carried out exactly (to
all orders in the non-commutative parameter) and analytically in two dimensions
for a free particle and a harmonic oscillator moving in a constant magnetic
field. We discuss the significance of the Seiberg-Witten map in this context.
It is shown for the harmonic oscillator potential that an approximate duality,
valid in the low energy sector, can be constructed between the interacting
commutative and a non-interacting non-commutative Hamiltonian. This
approximation holds to order 1/B and is therefore valid in the case of strong
magnetic fields and weak Landau-level mixing.Comment: 11 pages, no figure
Twisted Galilean symmetry and the Pauli principle at low energies
We show the twisted Galilean invariance of the noncommutative parameter, even
in presence of space-time noncommutativity. We then obtain the deformed algebra
of the Schr\"odinger field in configuration and momentum space by studying the
action of the twisted Galilean group on the non-relativistic limit of the
Klein-Gordon field. Using this deformed algebra we compute the two particle
correlation function to study the possible extent to which the previously
proposed violation of the Pauli principle may impact at low energies. It is
concluded that any possible effect is probably well beyond detection at current
energies.Comment: 16 pages Latex, 2 figures Some modifications made in the abstract,
introduction, typographical errors correcte
Seiberg-Witten map and Galilean symmetry violation in a non-commutative planar system
An effective U(1) gauge invariant theory is constructed for a non-commutative
Schrodinger field coupled to a background U(1)_{\star} gauge field in
2+1-dimensions using first order Seiberg-Witten map. We show that this
effective theory can be cast in the form of usual Schrodinger action with
interaction terms of noncommutative origin provided the gauge field is of
``background'' type with constant magnetic field. The Galilean symmetry is
investigated and a violation is found in the boost sector. We also consider the
problem of Hall conductivity in this framework.Comment: REVTeX, 4 pages, Title changed, Paper shortened, Appendix removed, A
new section on Galilean symmetry adde
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