41,003 research outputs found
On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions
In this work we consider de Branges spaces where the multiplication operator
by the independent variable is not densely defined. First, we study the
canonical selfadjoint extensions of the multiplication operator as a family of
rank-one perturbations from the viewpoint of the theory of de Branges spaces.
Then, on the basis of the obtained results, we provide new necessary and
sufficient conditions for a real, zero-free function to lie in a de Branges
space.Comment: 13 pages, no fugures. Theorem and remark have been added,
typographical erros correcte
Towards Noncommutative Linking Numbers Via the Seiberg-Witten Map
In the present work some geometric and topological implications of
noncommutative Wilson loops are explored via the Seiberg-Witten map. In the
abelian Chern-Simons theory on a three dimensional manifold, it is shown that
the effect of noncommutativity is the appearance of new knots at the
-th order of the Seiberg-Witten expansion. These knots are trivial homology
cycles which are Poincar\'e dual to the high-order Seiberg-Witten potentials.
Moreover the linking number of a standard 1-cycle with the Poincar\'e dual of
the gauge field is shown to be written as an expansion of the linking number of
this 1-cycle with the Poincar\'e dual of the Seiberg-Witten gauge fields. In
the process we explicitly compute the noncommutative 'Jones-Witten' invariants
up to first order in the noncommutative parameter. Finally in order to exhibit
a physical example, we apply these ideas explicitly to the Aharonov-Bohm
effect. It is explicitly displayed at first order in the noncommutative
parameter, we also show the relation to the noncommutative Landau levels.Comment: 19 pages, 1 figur
Singular Schroedinger operators as self-adjoint extensions of n-entire operators
We investigate the connections between Weyl-Titchmarsh-Kodaira theory for
one-dimensional Schr\"odinger operators and the theory of -entire operators.
As our main result we find a necessary and sufficient condition for a
one-dimensional Schr\"odinger operator to be -entire in terms of square
integrability of derivatives (w.r.t. the spectral parameter) of the Weyl
solution. We also show that this is equivalent to the Weyl function being in a
generalized Herglotz-Nevanlinna class. As an application we show that perturbed
Bessel operators are -entire, improving the previously known conditions on
the perturbation.Comment: 14 page
The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions
We study the nonrelativistic limit of the theory of a quantum Chern--Simons
field minimally coupled to Dirac fermions. To get the nonrelativistic effective
Lagrangian one has to incorporate vacuum polarization and anomalous magnetic
moment effects. Besides that, an unsuspected quartic fermionic interaction may
also be induced. As a by product, the method we use to calculate loop diagrams,
separating low and high loop momenta contributions, allows to identify how a
quantum nonrelativistic theory nests in a relativistic one.Comment: 18 pages, 8 figures, Late
Duality Symmetry in the Schwarz-Sen Model
The continuous extension of the discrete duality symmetry of the Schwarz-Sen
model is studied. The corresponding infinitesimal generator turns out to be
local, gauge invariant and metric independent. Furthermore, commutes with
all the conformal group generators. We also show that is equivalent to the
non---local duality transformation generator found in the Hamiltonian
formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky
formalism for the Maxwell theory and demonstrate that requiring a local duality
transformation lead us to the Schwarz--Sen formulation. The partition functions
are shown to be the same which implies the quantum equivalence of the two
approaches.Comment: 10 pages, latex, small changes, final version to appear in Phys. Rev.
Canonical Quantization of the Maxwell-Chern-Simons Theory in the Coulomb Gauge
The Maxwell-Chern-Simons theory is canonically quantized in the Coulomb gauge
by using the Dirac bracket quantization procedure. The determination of the
Coulomb gauge polarization vector turns out to be intrincate. A set of quantum
Poincar\'e densities obeying the Dirac-Schwinger algebra, and, therefore, free
of anomalies, is constructed. The peculiar analytical structure of the
polarization vector is shown to be at the root for the existence of spin of the
massive gauge quanta.The Coulomb gauge Feynman rules are used to compute the
M\"oller scattering amplitude in the lowest order of perturbation theory. The
result coincides with that obtained by using covariant Feynman rules. This
proof of equivalence is, afterwards, extended to all orders of perturbation
theory. The so called infrared safe photon propagator emerges as an effective
propagator which allows for replacing all the terms in the interaction
Hamiltonian of the Coulomb gauge by the standard field-current minimal
interaction Hamiltonian.Comment: 21 pages, typeset in REVTEX, figures not include
Large angle magnetization dynamics measured by time-resolved ferromagnetic resonance
A time-resolved ferromagnetic resonance technique was used to investigate the
magnetization dynamics of a 10 nm thin Permalloy film. The experiment consisted
of a sequence of magnetic field pulses at a repetition rate equal to the
magnetic systems resonance frequency. We compared data obtained by this
technique with conventional pulsed inductive microwave magnetometry. The
results for damping and frequency response obtained by these two different
methods coincide in the limit of a small angle excitation. However, when
applying large amplitude field pulses, the magnetization had a non-linear
response. We speculate that one possible cause of the nonlinearity is related
to self-amplification of incoherence, known as the Suhl instabilities.Comment: 23 pages, 8 figures, submitted to PR
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