1,118 research outputs found
Localization and real Jacobi forms
We calculate the elliptic genus of two dimensional abelian gauged linear
sigma models with (2,2) supersymmetry using supersymmetric localization. The
matter sector contains charged chiral multiplets as well as Stueckelberg fields
coupled to the vector multiplets. These models include theories that flow in
the infrared to non-linear sigma models with target spaces that are non-compact
Kahler manifolds with U(N) isometry and with an asymptotically linear dilaton
direction. The elliptic genera are the modular completions of mock Jacobi forms
that have been proposed recently using complementary arguments. We also compute
the elliptic genera of models that contain multiple Stueckelberg fields from
first principles.Comment: 19+1 pages, LaTeX. Minor correctio
PT-Symmetric Quantum Electrodynamics and Unitarity
More than 15 years ago, a new approach to quantum mechanics was suggested, in
which Hermiticity of the Hamiltonian was to be replaced by invariance under a
discrete symmetry, the product of parity and time-reversal symmetry,
. It was shown that if is unbroken, energies were,
in fact, positive, and unitarity was satisifed. Since quantum mechanics is
quantum field theory in 1 dimension, time, it was natural to extend this idea
to higher-dimensional field theory, and in fact an apparently viable version of
-invariant quantum electrodynamics was proposed. However, it has
proved difficult to establish that the unitarity of the scattering matrix, for
example, the K\"all\'en spectral representation for the photon propagator, can
be maintained in this theory. This has led to questions of whether, in fact,
even quantum mechanical systems are consistent with probability conservation
when Green's functions are examined, since the latter have to possess physical
requirements of analyticity. The status of QED will be reviewed
in this report, as well as the general issue of unitarity.Comment: 13 pages, 2 figures. Revised version includes new evidence for the
violation of unitarit
How Social Media Analytics Can Inform Social Content Strategies: Evidence from Healthcare Sector
Repulsive Casimir and Casimir-Polder Forces
Casimir and Casimir-Polder repulsion have been known for more than 50 years.
The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs
permits repulsion if they are separated by a dielectric fluid that has a value
of permittivity that is intermediate between those of the dielectric slabs.
This was indirectly confirmed in the 1970s, and more directly by Capasso's
group recently. It has also been known for many years that electrically and
magnetically polarizable bodies can experience a repulsive quantum vacuum
force. More amenable to practical application are situations where repulsion
could be achieved between ordinary conducting and dielectric bodies in vacuum.
The status of the field of Casimir repulsion with emphasis on recent
developments will be surveyed. Here, stress will be placed on analytic
developments, especially of Casimir-Polder (CP) interactions between
anisotropically polarizable atoms, and CP interactions between anisotropic
atoms and bodies that also exhibit anisotropy, either because of anisotropic
constituents, or because of geometry. Repulsion occurs for wedge-shaped and
cylindrical conductors, provided the geometry is sufficiently asymmetric, that
is, either the wedge is sufficiently sharp or the atom is sufficiently far from
the cylinder.Comment: 24 pages, 14 figures, contribution to the special issue of J. Phys. A
honoring Stuart Dowker. This revision corrects typos and adds additional
references and discussio
Disturbance decoupling problem for multi-agent systems:A graph topological approach
Çamlıbel, Mehmet Kanat (Dogus Author)This paper studies the disturbance decoupling problem for multi-agent systems with single integrator dynamics and a directed communication graph. We are interested in topological conditions that imply the disturbance decoupling of the network, and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled. In particular, we will develop a class of graph partitions, which can be described as a "topological translation" of controlled invariant subspaces in the context of dynamical networks. Then, we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled, as well as conditions guaranteeing solvability of the disturbance decoupling problem. The proposed results are illustrated by a numerical example
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