33,252 research outputs found
Global analysis by hidden symmetry
Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when is -spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda
Spontaneous CP Symmetry Breaking at the Electroweak Scale
We present a top-condensation model in which the CP symmetry is spontaneously
broken at the electroweak scale due to the condensation of two composite Higgs
doublets. In particular the CP-violating phase of the CKM matrix is generated.
A simpler model where only one quark family is included is also discussed. In
this case, for a general four-fermion interaction (), the
particle spectrum is the one of the one Higgs doublet model.Comment: 25 pages, LaTeX. References and comment adde
Special functions associated to a certain fourth order differential equation
We develop a theory of "special functions" associated to a certain fourth
order differential operator on depending
on two parameters . For integers with
this operator extends to a self-adjoint operator on
with discrete spectrum. We find a closed
formula for the generating functions of the eigenfunctions, from which we
derive basic properties of the eigenfunctions such as orthogonality,
completeness, -norms, integral representations and various recurrence
relations.
This fourth order differential operator arises as the
radial part of the Casimir action in the Schr\"odinger model of the minimal
representation of the group , and our "special functions" give
-finite vectors
Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
The existence of states enjoying a weak form of the Reeh-Schlieder property
has been recently established on curved backgrounds and in the framework of
locally covariant quantum field theory. Since only the example of a real scalar
field has been discussed, we extend the analysis to the case of massive and
massless free fields either of spin 1/2 or of spin 1. In the process, it is
also shown that both the vector potential and the Proca field can be described
as a locally covariant quantum field theory.Comment: 28 pages, references and remarks added, typos correcte
Double noding technique for mixed mode crack propagation studies
A simple dynamic finite element algorithm for analyzing a propagating mixed mode crack tip is presented. A double noding technique, which can be easily incorporated into existing dynamic finite element codes, is used together with a corrected J integral to extract modes I and II dynamic stress intensity factors of a propagating crack. The utility of the procedure is demonstrated by analyzing test problems involving a mode I central crack propagating in a plate subjected to uniaxial tension, a mixed mode I and II stationary, slanted central crack in a plate subjected to uniaxial impact loading, and a mixed mode I and II extending, slanted single edge crack in a plate subjected to uniaxial tension
A constructive algorithm for the Cartan decomposition of SU(2^N)
We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser
decomposition of a general element G of SU(2^N) in terms of its `Cartan' and
`non-Cartan' components. This effectively factors G in terms of group elements
that belong in SU(2^n) with n<N, a procedure that can be iterated down to n=2.
We show that every step reduces to solving the zeros of a matrix polynomial,
obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically.
All computational tasks involved are straightforward and the overall truncation
errors are well under control.Comment: 15 pages, no figures, matlab file at
http://cam.qubit.org/users/jiannis
First-principles calculations of step formation energies and step interactions on TiN(001)
We study the formation energies and repulsive interactions of monatomic steps
on the TiN(001) surface, using density functional total-energy calculations.
The calculated formation energy of [100] oriented steps agree well with
recently reported experimental values; these steps are shown to have a rumpled
structure, with the Ti atoms undergoing larger displacements than the N atoms.
For steps that are parallel to [110], our calculations predict a nitrogen (N)
termination, as the corresponding formation energy is several hundred meV/\AA \
smaller than that of Ti-terminated steps
Gauge Theories in Noncommutative Homogeneous K\"ahler Manifolds
We construct a gauge theory on a noncommutative homogeneous K\"ahler
manifold, where we employ the deformation quantization with separation of
variables for K\"ahler manifolds formulated by Karabegov. A key point in this
construction is to obtaining vector fields which act as inner derivations for
the deformation quantization. We show that these vector fields are the only
Killing vector fields. We give an explicit construction of this gauge theory on
noncommutative and noncommutative .Comment: 27 pages, typos correcte
Compensation of Effective Field in the Field-Induced Superconductor k-(BETS)2FeBr4 Observed by 77Se NMR
We report results of 77Se NMR frequency shift in the normal state of the
organic charge-transfer-salt k-(BETS)2FeBr4 which shows magnetic field-induced
superconductivity (FISC). From a simple mean field analysis, we determined the
field and the temperature dependences of the magnetization m_{pi} of the \pi
conduction electrons on BETS molecules. We found that the Fe spins are
antiferromagnetically coupled to the pi electrons and determined the exchange
field to be J = -2.3T/mu_B. The exchange field from the fully saturated Fe
moments (5 mu_B) is compensated by an external field of 12T. This is close to
the central field of the FISC phase, consistent with the Jaccarino-Peter local
field-compensation mechanism for FISC (Phys. Rev. Lett. 9, 290 (1962))
Bounds on gamma from CP violation measurements in B -> pi+ pi- and B -> psi K_S
We study the determination of gamma from CP-violating observables in B -> pi+
pi- and B -> psi K_S. This determination requires theoretical input to one
combination of hadronic parameters. We show that a mild assumption about this
quantity may allow bounds to be placed on gamma, but we stress the pernicious
effects that an eightfold discrete ambiguity has on such an analysis. The
bounds are discussed as a function of the direct (C) and interference (S)
CP-violating observables obtained from time-dependent B -> pi+ pi- decays, and
their behavior in the presence of new physics effects in B-Bbar mixing is
studied. (V2: Misprints corrected. Slightly improved discussion.)Comment: 11 pages, RevTex 4, 5 eps figures include
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