Publications (25)23.08 Total impact
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ABSTRACT: A state vector description for relativistic resonances is derived from the first order pole of the jth partial Smatrix at the invariant square mass value in the second sheet of the Riemann energy surface. To associate a ket, called Gamow vector, to the pole, we use the generalized eigenvectors of the fourvelocity operators in place of the customary momentum eigenkets of Wigner, and we replace the conventional Hilbert space assumptions for the in and outscattering states with the new hypothesis that in and outstates are described by two different Hardy spaces with complementary analyticity properties. The Gamow vectors have the following properties: (i) They are simultaneous generalized eigenvectors of the four velocity operators with real eigenvalues and of the selfadjoint invariant mass operator M =(Pμ Pμ)1/2 with complex eigenvalue . (ii) They have a Breit–Wigner distribution in the invariant square mass variable and lead to an exactly exponential law for the decay rates and probabilities.International Journal of Modern Physics A 01/2012; 17(26). DOI:10.1142/S0217751X02010868 · 1.70 Impact Factor 
Article: QCD on the Cell Broadband Engine
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ABSTRACT: We evaluate IBM's Enhanced Cell Broadband Engine (BE) as a possible building block of a new generation of lattice QCD machines. The Enhanced Cell BE will provide full support of doubleprecision floatingpoint arithmetics, including IEEEcompliant rounding. We have developed a performance model and applied it to relevant lattice QCD kernels. The performance estimates are supported by micro and applicationbenchmarks that have been obtained on currently available Cell BEbased computers, such as IBM QS20 blades and PlayStation 3. The results are encouraging and show that this processor is an interesting option for lattice QCD applications. For a massively parallel machine on the basis of the Cell BE, an applicationoptimized network needs to be developed.  [Show abstract] [Hide abstract]
ABSTRACT: Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times. This provides the means of demonstrating the beginning of time of a semigroup evolution for a decaying state. 
Article: Time Asymmetry in Quantum Physics  I. Theoretical Conclusion from Resonance and DecayPhenomenology
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ABSTRACT: It is explained how the unification of resonance and decay phenomena into a consistent mathematical theory leads to quantum mechanical timeasymmetry. This provides the theoretical basis for a subsequent paper II in which the interpretation and experimental demonstration of this timeasymmetry is discussed. 
Article: Calculation of the Scattering Amplitude for Resonance Production using Relativistic Gamow Vectors
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ABSTRACT: This paper has been withdrawn by the author in order to implement the referee's suggestions and comments. Comment: The paper has been withdrawn  [Show abstract] [Hide abstract]
ABSTRACT: The calculation of an amplitude involving resonance production is presented. This calculation employs for the resonance state a relativistic Gamow vector. It is used for investigating the question of compatibility of the relativistic Gamow vectors kinematics, defined by real 4velocities and complex mass, with the stable particle kinematics; or in other words, the integration of the Gamow vectors with the conventional Dirac braket formalism. The calculation demonstrates a consistent framework comprising stable and Gamow vectors. 
Article: The apeNEXT project
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ABSTRACT: In this talk I report on the status of the apeNEXT project. apeNEXT is the last of a family of parallel computers designed, in a research environment, to provide multiteraflops computing power to scientists involved in heavy numerical simulations. The architecture and the custom chip are optimized for Lattice QCD (LQCD) calculations but the favourable price performance ratio and the good efficiency for other kind of calculations make it a quite interesting tool for a large class of scientific problems.Nuclear Physics B  Proceedings Supplements 02/2005; 140(1):176182. DOI:10.1016/j.nuclphysbps.2004.11.359 · 0.88 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present the APE (Array Processor Experiment) project for the development of dedicated parallel computers for numerical simulations in lattice gauge theories. While APEmille is a production machine in today's physics simulations at various sites in Europe, a new machine, apeNEXT, is currently being developed to provide multiTflops computing performance. Like previous APE machines, the new supercomputer is largely custom designed and specifically optimized for simulations of Lattice QCD. Comment: Poster at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 3 pages, Latex. PSN FRAP15. Replaced for adding forgotten author 
Article: The apeNEXT project (Status report)
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ABSTRACT: We present the current status of the apeNEXT project. Aim of this project is the development of the next generation of APE machines which will provide multiteraflop computing power. Like previous machines, apeNEXT is based on a custom designed processor, which is specifically optimized for simulating QCD. We discuss the machine design, report on benchmarks, and give an overview on the status of the software development. Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 8 pages, LaTeX, 12 eps figures. PSN THIT005  [Show abstract] [Hide abstract]
ABSTRACT: A relativistic resonance which was defined by a pole of the $S$matrix, or by a relativistic BreitWigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic LippmannSchwinger kets. These Gamow kets span an irreducible representation space for Poincar\'e transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincar\'e transformations of the Gamow kets, as well as of the LippmannSchwinger plane wave scattering states, form only a semigroup of Poincar\'e transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed. Comment: 49 pages, 1 figureFortschritte der Physik 06/2003; 51(6). DOI:10.1002/prop.200310075 · 2.44 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Relativistic resonances and decaying states are described by representations of Poincar\'e transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in and outscattering states. Then one can separate the scattering amplitude into a background amplitude and one or several ``relativistic BreitWigner'' amplitudes, which represent the resonances per se. These BreitWigner amplitudes have a precisely defined lineshape and are associated to exponentially decaying Gamow vectors which furnish the irreducible representation spaces of causal Poincar\'e transformations into the forward light cone. Comment: 57 pages, 6 figuresFortschritte der Physik 06/2003; 51(6). DOI:10.1002/prop.200310074 · 2.44 Impact Factor 
Conference Paper: apeNEXT: a MultiTFlops Computer for Elementary Particle Physics.
Parallel Computing: Software Technology, Algorithms, Architectures and Applications, PARCO 2003, Dresden, Germany; 01/2003 
Article: Status of the apeNEXT project
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ABSTRACT: We present the current status of the apeNEXT project. Aim of this project is the development of the next generation of APE machines which will provide multiteraflop computing power. Like previous machines, apeNEXT is based on a custom designed processor, which is specifically optimized for simulating QCD. We discuss the machine design, report on benchmarks, and give an overview on the status of the software development. Comment: 3 pages, Lattice2002(machines). Replaced for adding forgotten authorNuclear Physics B  Proceedings Supplements 11/2002; 119:1038. DOI:10.1016/S09205632(03)017559 · 0.88 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: APE is a family of supercomputers architecturally optimized for the numerical simulation of quantum field theories. Current generation APE systems (APEmille) have been commissioned at several European sites. When all planned systems are installed, later this year, a total peak processing power of about 2 TFlops will be available. A new generation system, apeNEXT, is under development. It adds several new features to the established APE architecture. Performance will be boosted towards the 10 Tflops range.Computer Physics Communications 08/2002; 147(s 1–2):402–409. DOI:10.1016/S00104655(02)003144 · 3.11 Impact Factor 
Article: The apeNEXT project
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ABSTRACT: APENEXT is a new generation APE processor, optimized for LGT simulations. The project follows the basic ideas of previous APE machines and develops simple and cheap parallel systems with multi TFlops processing power. This paper describes the main features of this new development. Comment: Lattice2001(plenary/machinestatus), 4 pages, 1 eps figureNuclear Physics B  Proceedings Supplements 10/2001; 106:173. DOI:10.1016/S09205632(01)016565 · 0.88 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A state vector description for relativistic resonances is derived from the first order pole of the $j$th partial $S$matrix at the invariant square mass value $\sm_R=(mi\Gamma/2)^2$ in the second sheet of the Riemann energy surface. To associate a ket, called Gamow vector, to the pole, we use the generalized eigenvectors of the fourvelocity operators in place of the customary momentum eigenkets of Wigner, and we replace the conventional Hilbert space assumptions for the in and outscattering states with the new hypothesis that in and outstates are described by two different Hardy spaces with complementary analyticity properties. The Gamow vectors have the following properties:  They are simultaneous generalized eigenvectors of the four velocity operators with real eigenvalues and of the selfadjoint invariant mass operator $M=(P_\mu P^\mu)^{1/2}$ with complex eigenvalue $\sqrt{\sm_R}$.  They have a BreitWigner distribution in the invariant square mass variable $\sm$ and lead to an exactly exponential law for the decay rates and probabilities.  [Show abstract] [Hide abstract]
ABSTRACT: Relativistic Gamow vectors emerge naturally in a time asymmetric quantum theory as the covariant kets associated to the resonance pole in the second sheet of the analytically continued Smatrix. They are eigenkets of the selfadjoint mass operator with complex eigenvalue and have exponential time evolution with lifetime . If one requires that the resonance width (defined by the BreitWigner lineshape) and the resonance lifetime always and exactly fulfill the relation , then one is lead to the following parameterization of in terms of resonance mass and width : . Applying this result to the boson implies that and GR » GZ1.2MeV\Gamma_R \approx \Gamma_Z1.2\mbox{MeV} are the mass and width of the {\it Z}boson and not the particle data values or any other parameterization of the Zboson lineshape. Furthermore, the transformation properties of these Gamow kets show that they furnish an irreducible representation of the causal Poincaré semigroup, defined as a semidirect product of the homogeneous Lorentz group with the semigroup of spacetime translations into the forward light cone. Much like Wigner's unitary irreducible representations of the Poincaré group which describe stable particles, these irreducible semigroup representations can be characterized by the spinmass values .European Physical Journal C 01/2000; 18(2):333342. DOI:10.1007/s100520000411 · 5.08 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Gamow vectors are generalized eigenvectors (kets) of selfadjoint Hamiltonians with complex eigenvalues (ER /+ i Gamma/2) describing quasistable states. In the relativistic domain this leads to Poincare semigroup representations which are describing quasistable states. In the relativistic domain this leads to Poincare a characterized by spin j and by complex invariant mass square s = s(R) = ( MR  1/2 Gamma(R))(2). Relativistic Gamow kets have all the properties required to describe relativistic resonances and quasistable particles with resonance mass MR and lifetime h/Gamma(R).Physics Letters A 01/2000; 264(6264):425433. DOI:10.1016/S03759601(99)008294 · 1.68 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is reviewed and contrasted with the standard Hilbert space (HS) theory of quantum mechanics. The main difference is in the choice of boundary conditions. Whereas the conventional theory allows for the instates $\phi^+$ and the outstates (observables) $\psi^$ of the Smatrix elements $(\psi^,\phi^+)=(\psi^{out},S \phi^{in})$ any elements of the HS $\H$, $\{\psi^\}=\{\phi^+\}(=\H)$, the RHS theory chooses the boundary conditions~: $\phi^+\in\Phi_\subset\H\subset\Phi_^\times$, $\psi^\in\Phi_+\subset \H\subset \Phi_+^\times$, where $\Phi_$ ($\Phi_+$) are Hardy class spaces associated to the lower (upper) halfplane of the second sheet of the analytically continued Smatrix. This can be phenomenologically justified by causality. The two RHS's for states $\phi^+$ and observables $\psi^$ provide new vectors which are not in $\H$, e.g. the DiracLippmannSchwinger kets $E^{\pm}\in\Phi_{\mp}^{\times}$ (solutions of the LippmannSchwinger equation with $\pm i\epsilon$ respectively) and the Gamow vectors $E_Ri\Gamma/2^\pm\in\Phi_{\mp}^\times$. The Gamow vectors $E_Ri\Gamma/2^$ have all the properties that one heuristically needs for quasistable states. In addition, they give rise to asymmetric time evolution expressing irreversibility on the microphysical level. 
Article: Relativistic Gamow Vectors II
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ABSTRACT: Motivated by the debate of possible definitions of mass and width of resonances for $Z$boson and hadrons, we suggest a definition of unstable particles by ``minimally complex'' semigroup representations of the Poincar\'e group characterized by $(j,{\mathsf s}=(mi\Gamma/2)^{2})$ in which the Lorentz subgroup is unitary. This definition, though decidedly distinct from those based on various renormalization schemes of perturbation theory, is intimately connected with the first order pole definition of the $S$matrix theory in that the complex square mass $(mi\Gamma/2)^{2}$ characterizing the representation of the Poincar\'e semigroup is exactly the position ${\mathsf s}_R$ at which the $S$matrix has a simple pole. Wigner's representations $(j,m)$ are the limit case of the complex representations for $\Gamma=0$. These representations have generalized vectors (Gamow kets) which have, in addition to the $S$matrix pole at ${\mathsf s}=(mi\Gamma/2)^{2}$, all the other properties that heuristically the unstable states need to possess: a BreitWigner distribution in invariant square mass and a lifetime $\tau=\frac{1}{\Gamma}$ defined by the exactly exponential law for the decay probability ${\cal P}(t)$ and rate $\dot{\cal P}(t)$ given by an exact Golden Rule which becomes Dirac's Golden Rule in the Bornapproximation. In addition and unintended, they have an asymmetric time evolution.
Publication Stats
167  Citations  
23.08  Total Impact Points  
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Institutions

19992012

University of Texas at Austin
 Department of Physics
Austin, Texas, United States


20012005

Deutsches ElektronenSynchrotron
Hamburg, Hamburg, Germany
