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 $X_C$ is $G_C$-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 ($G_{tb}\neq 0$), 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 $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ 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, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-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 ${\mathbb C}P^N$ and noncommutative ${\mathbb C}H^N$.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