Energy decay for the linear Klein-Gordon equation and boundary control

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

N=2 supersymmetric QCD and elliptic potentials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bianchi identities for an N=2, d=5 supersymmetric Yang-Mills theory on the group manifold

The purpose of this note is the construction of a geometrical structure for a supersymmetric N = 2, d = 5 Yang-Mills theory on the group manifold. From a general hypothesis proposed for the curvatures of the theory, the Bianchi identities are solved, whose solution will be fundamental for the construction of the geometrical action for the N = 2, d = 5 supergravity and Yang-Mills coupled theory.

Supersymmetric Isospectral Formalism for the Calculation of Near-Zero Energy States: Application to the Very Weakly Bound He-4 Trimer Excited State

We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in He-4 trimer is presented.

Supersymmetric extension of the quantum spherical model

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short- and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.

Dynamical (super)symmetry vacuum properties of the supersymmetric Chern-Simons-matter model

By computing the two-loop effective potential of the D=3 N=1 supersymmetric Chern-Simons model minimally coupled to a massless self-interacting matter superfield, it is shown that supersymmetry is preserved, while the internal U(1) and the scale symmetries are broken at two-loop order, dynamically generating masses both for the gauge superfield and for the real component of the matter superfield.

All-loop finiteness of the two-dimensional noncommutative supersymmetric gauge theory

Within the superfield approach, we discuss the two-dimensional noncommutative super-QED. Its all-order finiteness is explicitly shown. Copyright (C) EPLA, 2012

CP asymmetries in the supersymmetric trilepton signal at the LHC

In the CP-violating Minimal Supersymmetric Standard Model, we study the production of a neutralino-chargino pair at the LHC. For their decays into three leptons, we analyze CP asymmetries which are sensitive to the CP phases of the neutralino and chargino sector. We present analytical formulas for the entire production and decay process, and identify the CP-violating contributions in the spin correlation terms. This allows us to define the optimal CP asymmetries. We present a detailed numerical analysis of the cross sections, branching ratios, and the CP observables. For light neutralinos, charginos, and squarks, the asymmetries can reach several 10%. We estimate the discovery potential for the LHC to observe CP violation in the trilepton channel.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Supersymmetric Dark Matter : aspects of sfermion coannihilations

There is very strong evidence that ordinary matter in the Universe is outweighed by almost ten times as much so-called dark matter. Dark matter does neither emit nor absorb light and we do not know what it is. One of the theoretically favoured candidates is a so-called neutralino from the supersymmetric extension of the Standard Model of particle physics. A theoretical calculation of the expected cosmic neutralino density must include the so-called coannihilations. Coannihilations are particle processes in the early Universe with any two supersymmetric particles in the initial state and any two Standard Model particles in the final state. In this thesis we discuss the importance of these processes for the calculation of the relic density. We will go through some details in the calculation of coannihilations with one or two so-called sfermions in the initial state. This includes a discussion of Feynman diagrams with clashing arrows, a calculation of colour factors and a discussion of ghosts in non-Abelian field theory. Supersymmetric models contain a large number of free parameters on which the masses and couplings depend. The requirement, that the predicted density of cosmic neutralinos must agree with the density observed for the unknown dark matter, will constrain the parameters. Other constraints come from experiments which are not related to cosmology. For instance, the supersymmetric loop contribution to the rare b -> sγ decay should agree with the measured branching fraction. The principles of the calculation of the rare decay are discussed in this thesis. Also on-going and planned searches for cosmic neutralinos can constrain the parameters. In one of the accompanying papers in the thesis we compare the detection prospects for several current and future searches for neutralino dark matter.

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Dispersive wave solutions of the klein-gordon equation in cosmology

L'equazione di Klein-Gordon descrive una ampia varietà di fenomeni fisici come la propagazione delle onde in Meccanica dei Continui ed il comportamento delle particelle spinless in Meccanica Quantistica Relativistica. Recentemente, la forma dissipativa di questa equazione si è rivelata essere una legge di evoluzione fondamentale in alcuni modelli cosmologici, in particolare nell'ambito dei cosiddetti modelli di k-inflazione in presenza di campi tachionici. L'obiettivo di questo lavoro consiste nell'analizzare gli effetti del parametro dissipativo sulla dispersione nelle soluzioni dell'equazione d'onda. Saranno inoltre studiati alcuni tipici problemi al contorno di particolare interesse cosmologico per mezzo di grafici corrispondenti alle soluzioni fondamentali (Funzioni di Green).