22 research outputs found
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
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
Noncommutativity in interpolating string: A study of gauge symmetries in noncommutative framework
A new Lagrangian description that interpolates between the Nambu--Goto and
Polyakov version of interacting strings is given. Certain essential
modifications in the Poission bracket structure of this interpolating theory
generates noncommutativity among the string coordinates for both free and
interacting strings. The noncommutativity is shown to be a direct consequence
of the nontrivial boundary conditions. A thorough analysis of the gauge
symmetry is presented taking into account the new modified constraint algebra,
which follows from the noncommutative structures and finally a smooth
correspondence between gauge symmetry and reparametrisation is established.Comment: 14 pages Late
Normal ordering and non(anti)commutativity in open super strings
Nonanticommutativity in an open super string moving in the presence of a
background antisymmetric tensor field is investigated
in a conformal field theoretic approach, leading to nonanticommutative
structures. In contrast to several discussions, in which boundary conditions
are taken as Dirac constraints, we first obtain the mode algebra by using the
newly proposed normal ordering, which satisfies both equations of motion and
boundary conditions. Using these the anticommutator among the fermionic string
coordinates is obtained. Interestingly, in contrast to the bosonic case, this
new normal ordering plays an important role in uncovering the underlying
nonanticommutative structure between the fermionic string coordinates. We feel
that our approach is more transparent than the previous ones and the results we
obtain match with the existing results in the literature.Comment: Comments 10 pages latex, accepted for publication in Physical Review
Non(anti) commutativity for open superstrings
Non(anti)commutativity in an open free superstring and also one moving in a
background anti-symmetric tensor field is investigated. In both cases, the
non(anti)commutativity is shown to be a direct consequence of the non-trivial
boundary conditions which, contrary to several approaches, are not treated as
constraints. The above non(anti)commutative structures lead to new results in
the algebra of super constraints which still remain involutive, indicating the
internal consistency of our analysis.Comment: 10 pages Latex, To appear in Physics Letters
String non(anti)commutativity for Neveu-Schwarz boundary conditions
The appearance of non(anti)commutativity in superstring theory, satisfying
the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open
free superstring and also one moving in a background antisymmetric tensor field
are analyzed to illustrate the point that string non(anti)commutativity is a
consequence of the nontrivial boundary conditions. The method used here is
quite different from several other approaches where boundary conditions were
treated as constraints. An interesting observation of this study is that, one
requires that the bosonic sector satisfies Dirichlet boundary conditions at one
end and Neumann at the other in the case of the bosonic variables
being antiperiodic. The non(anti)commutative structures derived in this paper
also leads to the closure of the super constraint algebra which is essential
for the internal consistency of our analysis.Comment: new references added, original article appeared in Int.J.Theor.Phy