Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space

Lowest weight modules, in particular, Verma modules over the N = 1,2 super Schrodinger algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors. The classification of the irreducible lowest weight modules is given for both massive and massless representations. A vector field realization of the N = 1, 2 super Schrodinger algebras is also presented.Comment: 19 pages, no figur

Attachment and Reflective Functioning in Women With Borderline Personality Disorder

Insecure attachment and impairments in reflective functioning (RF) are thought to play a critical role in borderline personality disorder (BPD). In particular, the mentalization-based model argues that insecure attachment indirectly accounts for increased BPD features, notably via disruption of RF capacities. Although the mediation relationship between attachment, RF, and BPD is supported by previous evidence, it remains to be directly tested in adults with BPD. In the current study, a sample of 55 female adult BPD patients and 105 female healthy controls completed a battery of self-report measures to investigate the interplay between attachment, RF capacities, and BPD clinical status. Overall, the results showed that BPD patients predominantly reported insecure attachment, characterized by negative internal working models of the self as unlovable and unimportant to others, and decreased RF abilities. Our findings further indicated that actual RF capacities mediated the relationships between adult insecure attachment and BPD clinical status

Lowest weight representations of super Schrodinger algebras in low dimensional spacetime

We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all singular vectors within the Verma modules are constructed explicitly then irreducibility of the associated quotient modules is studied again by the use of singular vectors. We present the classification of irreducible Verma modules for the super Schrodinger algebras in (1+1) and (2+1) dimensional spacetime with N = 1, 2 extensions.Comment: 10pages, talk given at GROUP28 conference New Castle 26-30th July 2010, reference adde

Search for the Lepton-Number-Violating Decay Ξ−→pμ−μ−\Xi^- \to p \mu^- \mu^-

A sensitive search for the lepton-number-violating decay $\Xi^-\to p \mu^-\mu^-$ has been performed using a sample of $\sim10^9$ $\Xi^-$ hyperons produced in 800 GeV/$c$ $p$-Cu collisions. We obtain $\mathcal{B}(\Xi^-\to p \mu^-\mu^-)< 4.0\times 10^{-8}$ at 90% confidence, improving on the best previous limit by four orders of magnitude.Comment: 9 pages, 5 figures, to be published in Phys. Rev. Let

delta S = 2 nonleptonic hyperon decays

A sensitive search for the rare decays \Omega^- \to \Lambda \pi^- and \Xi^0 \to p \pi^- has been performed using data from the 1997 run of the HyperCP (Fermilab E871) experiment. Limits on other such processes do not exclude the possibility of observable rates for |\Delta S| = 2 nonleptonic hyperon decays, provided the decays occur through parity-odd operators. We obtain the branching-fraction limits B(\Omega^- \to \Lambda \pi^-)< 2.9 x 10^{-6} and B(\Xi^0 \to p \pi^-)< 8.2 x 10^{-6}, both at 90% confidence level.Comment: 4 pages, 5 figures, PRL pape

Observables and Correlators in Nonrelativistic ABJM Theory

Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N=6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator acting on spin chain is trivial at planar limit. These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string defined on it.Comment: 1+30 pages, no figure, v2. typos fixed and references adde

Observation of B+- -> omega K+- Decay

We report the first observation of the charmless two-body mode $B^{\pm} \to \omega K^{\pm}$ decay, and a new measurement of the branching fraction for the $B^{\pm} \to \omega \pi^{\pm}$ decay. The measured branching fractions are ${\cal B} (B^{\pm} \to \omega K^{\pm}) = (9.2{}^{+2.6}_{-2.3}\pm 1.0) \times 10^{-6}$ and ${\cal B} (B^{\pm} \to \omega \pi^{\pm}) = (4.2{}^{+2.0}_{-1.8}\pm 0.5) \times 10^{-6}$. %and we set 90% confidence level upper limits of %${\cal B} (B^- \to \omega \pi^-) < 8.1\times 10^{-6}$. We also measure the partial rate asymmetry of $B^{\pm}\to\omega K^{\pm}$ decays and obtain ${\cal A}_{CP} = -0.21 \pm 0.28 \pm 0.03$. The results are based on a data sample of 29.4 fb$^{-1}$ collected on the $\Upsilon(4S)$ resonance by the Belle detector at the KEKB $e^{+} e^{-}$ collider.Comment: 5 pages, 4 figures, resubmitted to Phys. Rev. Let

A class of solvable Lie algebras and their Casimir Invariants

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants of n_{n,1} and of its solvable extensions are calculated. For n=4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.Comment: 16 page

Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving branching-annihilating random walk, two exactly solvable particle-reaction models and kinetic growth models. While the generic scaling descriptions known from magnetic system can be taken over, some of the scaling relations between the ageing exponents are no longer valid. In particular, there is no obvious generalization of the universal limit fluctuation-dissipation ratio. The form of the scaling function of the two-time response function is compared with the prediction of the theory of local scale-invariance.Comment: Latex2e with IOP macros, 32 pages; extended discussion on contact process and new section on kinetic growth processe