7,562 research outputs found
Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
The Schroedinger operator with point interaction in one dimension has a U(2)
family of self-adjoint extensions. We study the spectrum of the operator and
show that (i) the spectrum is uniquely determined by the eigenvalues of the
matrix U belonging to U(2) that characterizes the extension, and that (ii) the
space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius
strip with boundary. We employ a parametrization of U(2) that admits a direct
physical interpretation and furnishes a coherent framework to realize the
spectral duality and anholonomy recently found. This allows us to find that
(iii) physically distinct point interactions form a three-parameter quotient
space of the U(2) family.Comment: 16 pages, 2 figure
Space-modulated Stability and Averaged Dynamics
In this brief note we give a brief overview of the comprehensive theory,
recently obtained by the author jointly with Johnson, Noble and Zumbrun, that
describes the nonlinear dynamics about spectrally stable periodic waves of
parabolic systems and announce parallel results for the linearized dynamics
near cnoidal waves of the Korteweg-de Vries equation. The latter are expected
to contribute to the development of a dispersive theory, still to come.Comment: Proceedings of the "Journ\'ees \'Equations aux d\'eriv\'ees
partielles", Roscoff 201
N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
We present a formulation of the maximally supersymmetric N=4 gauge theory in
Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor
formulation of the theory but employs the simpler notion of Lorentz harmonic
variables. They parametrize a two-sphere and allow us to handle efficiently
infinite towers of higher-spin auxiliary fields defined on ordinary space-time.
In this approach the chiral half of N=4 supersymmetry is manifest. The other
half is realized non-linearly and the algebra closes on shell. We give a
straightforward derivation of the Feynman rules in coordinate space. We show
that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably
similar to the harmonic superspace formulation of the N=2 gauge and
hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the
LHC formalism to the study of the non-chiral multipoint correlation functions
of the N=4 stress-tensor supermultiplet.Comment: 51 pages, 4 figures; v2: Appendix B on the propagators in momentum
space added. A more detailed comparison with the twistor approach given in
Appendix
Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
We present an anomaly-free Dirac constraint quantization of the
string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional
spacetime. We show that the quantum theory has the same degrees of freedom as
the classical theory; namely, all the modes of the scalar field on an auxiliary
flat background, supplemented by a single additional variable corresponding to
the primordial component of the black hole mass. The functional Heisenberg
equations of motion for these dynamical variables and their canonical
conjugates are linear, and they have exactly the same form as the corresponding
classical equations. A canonical transformation brings us back to the physical
geometry and induces its quantization.Comment: 37 pages, LATEX, no figures, submitted to Physical Review
Higher derivative extensions of Chern-Simons models: conservation laws and stability
We consider the class of higher derivative vector field models with the
field equation operator being a polynomial of the Chern-Simons operator. For
-th order theory of this type, we provide a general receipt for constructing
-parameter family of conserved second rank tensors. The family includes the
canonical energy-momentum tensor, which is unbounded, while there are bounded
conserved tensors that provide classical stability of the system for certain
combinations of the parameters in the Lagrangian. We also demonstrate the
examples of consistent interactions which are compatible with the requirement
of stability.Comment: 14 pages, minor correction
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