2,129,255 research outputs found
Symmetric photon-photon coupling by atoms with Zeeman-split sublevels
We propose a simple scheme for highly efficient nonlinear interaction between
two weak optical fields. The scheme is based on the attainment of
electromagnetically induced transparency simultaneously for both fields via
transitions between magnetically split F=1 atomic sublevels, in the presence of
two driving fields. Thereby, equal slow group velocities and symmetric
cross-coupling of the weak fields over long distances are achieved. By simply
tuning the fields, this scheme can either yield giant cross-phase modulation or
ultrasensitive two-photon switching.Comment: Modified scheme, 4 pages, 1 figur
Nonlinear Realization of the Local Conform-Affine Symmetry Group for Gravity in the Composite Fiber Bundle Formalism
A gauge theory of gravity based on a nonlinear realization (NLR) of the local
Conform-Affine (CA) group of symmetry transformations is presented. The coframe
fields and gauge connections of the theory are obtained. The tetrads and
Lorentz group metric are used to induce a spacetime metric. The inhomogenously
transforming (under the Lorentz group) connection coefficients serve as
gravitational gauge potentials used to define covariant derivatives
accommodating minimal coupling of matter and gauge fields. On the other hand,
the tensor valued connection forms serve as auxillary dynamical fields
associated with the dilation, special conformal and deformational (shear)
degrees of freedom inherent in the bundle manifold. The bundle curvature of the
theory is determined. Boundary topological invariants are constructed. They
serve as a prototype (source free) gravitational Lagrangian. The Bianchi
identities, covariant field equations and gauge currents are obtained.Comment: 24 pages. to appear in IJGMM
(Supersymmetric) Kac-Moody Gauge Fields in 3+1 Dimensions
Lagrangians for gauge fields and matter fields can be constructed from the
infinite dimensional Kac-Moody algebra and group. A continuum regularization is
used to obtain such generic lagrangians, which contain new nonlinear and
asymmetric interactions not present in gauge theories based on compact Lie
groups. This technique is applied to deriving the Yang-Mills and Chern-Simons
lagrangians for the Kac-Moody case. The extension of this method to D=4,
N=(1/2,0) supersymmetric Kac-Moody gauge fields is also made.Comment: 21 pages, no figures, latex. Minor change
Interacting Quantum Topologies and the Quantum Hall Effect
The algebra of observables of planar electrons subject to a constant
background magnetic field B is given by A_theta(R^2) x A_theta(R^2) the product
of two mutually commuting Moyal algebras. It describes the free Hamiltonian and
the guiding centre coordinates. We argue that A_theta(R^2) itself furnishes a
representation space for the actions of these two Moyal algebras, and suggest
physical arguments for this choice of the representation space. We give the
proper setup to couple the matter fields based on A_theta(R^2) to
electromagnetic fields which are described by the abelian commutative gauge
group G_c(U(1)), i.e. gauge fields based on A_0(R^2). This enables us to give a
manifestly gauge covariant formulation of integer quantum Hall effect (IQHE).
Thus, we can view IQHE as an elementary example of interacting quantum
topologies, where matter and gauge fields based on algebras A_theta^prime with
different theta^prime appear. Two-particle wave functions in this approach are
based on A_theta(R^2) x A_theta(R^2). We find that the full symmetry group in
IQHE, which is the semi-direct product SO(2) \ltimes G_c(U(1)) acts on this
tensor product using the twisted coproduct Delta_theta. Consequently, as we
show, many particle sectors of each Landau level have twisted statistics. As an
example, we find the twisted two particle Laughlin wave functions.Comment: 10 pages, LaTeX, Corrected typos, Published versio
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