The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Ivo Sachs - One of the best experts on this subject based on the ideXlab platform.
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open superstring field theory on the restricted Hilbert Space
Journal of High Energy Physics, 2016Co-Authors: Sebastian Konopka, Ivo SachsAbstract:It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert Space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert Space with other approaches and to formulate open superstring field theory entirely in the small Hilbert Space.
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open superstring field theory on the restricted Hilbert Space
arXiv: High Energy Physics - Theory, 2016Co-Authors: Sebastian Konopka, Ivo SachsAbstract:Recently an action for open superstring field theory was proposed where the Neveu-Schwarz sector is formulated in the large Hilbert Space while the Ramond sector lives in a restriction of the small Hilbert Space. The purpose of this note is to clarify the relation of the restricted Hilbert Space with other approaches and to formulate open superstring field theory entirely in the small Hilbert Space.
R De La Madrid - One of the best experts on this subject based on the ideXlab platform.
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The rigged Hilbert Space approach to the Lippmann–Schwinger equation: Part I
Journal of Physics A: Mathematical and General, 2006Co-Authors: R De La MadridAbstract:We exemplify the way the rigged Hilbert Space deals with the Lippmann?Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann?Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert Spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann?Schwinger equation?and therefore for scattering theory?is the rigged Hilbert Space rather than just the Hilbert Space.
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The role of the rigged Hilbert Space in Quantum Mechanics
European Journal of Physics, 2005Co-Authors: R De La MadridAbstract:There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert Space rather than just the Hilbert Space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert Space rather than just by the Hilbert Space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert Space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert Space.
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Rigged Hilbert Space approach to the Schrödinger equation
Journal of Physics A, 2002Co-Authors: R De La MadridAbstract:It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the rigged Hilbert Space (RHS) rather than just the Hilbert Space. The difficulties of using only the Hilbert Space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate RHS. The RHS is able to associate an eigenket with each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wavefunction. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.
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Rigged Hilbert Space Treatment of Continuous Spectrum
Fortschritte der Physik, 2002Co-Authors: R De La Madrid, Arno Bohm, Manuel GadellaAbstract:The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrodinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the Space of physical wave functions. They are also basis vectors that expand any physical wave function in a Dirac basis vector expansion. It is shown that an acceptable physical wave function must fulfill stronger conditions than just square integrability--the Space of physical wave functions is not the whole Hilbert Space but rather a dense subSpace of the Hilbert Space. We construct the position and energy representations of the Rigged Hilbert Space generated by the square barrier potential Hamiltonian. We shall also construct the unitary operator that transforms from the position into the energy representation. We shall see that in the energy representation the Dirac kets act as the antilinear Schwartz delta functional. In constructing the Rigged Hilbert Space of the square barrier potential, we will find a systematic procedure to construct the Rigged Hilbert Space of a large class of spherically symmetric potentials. The example of the square barrier potential will also make apparent that the natural framework for the solutions of a Schrodinger operator with continuous spectrum is the Rigged Hilbert Space rather than just the Hilbert Space.
Sebastian Konopka - One of the best experts on this subject based on the ideXlab platform.
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open superstring field theory on the restricted Hilbert Space
Journal of High Energy Physics, 2016Co-Authors: Sebastian Konopka, Ivo SachsAbstract:It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert Space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert Space with other approaches and to formulate open superstring field theory entirely in the small Hilbert Space.
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open superstring field theory on the restricted Hilbert Space
arXiv: High Energy Physics - Theory, 2016Co-Authors: Sebastian Konopka, Ivo SachsAbstract:Recently an action for open superstring field theory was proposed where the Neveu-Schwarz sector is formulated in the large Hilbert Space while the Ramond sector lives in a restriction of the small Hilbert Space. The purpose of this note is to clarify the relation of the restricted Hilbert Space with other approaches and to formulate open superstring field theory entirely in the small Hilbert Space.
A. Zee - One of the best experts on this subject based on the ideXlab platform.
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Is Hilbert Space discrete
Physics Letters B, 2005Co-Authors: Roman V. Buniy, Stephen D. H. Hsu, A. ZeeAbstract:We show that discretization of Spacetime naturally suggests discretization of Hilbert Space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert Space is discrete. We give some simple examples involving qubits and the Schrodinger wavefunction, and discuss implications for quantum information and quantum gravity.
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Is Hilbert Space discrete?
Physics Letters B, 2005Co-Authors: Roman V. Buniy, Stephen D. H. Hsu, A. ZeeAbstract:We show that discretization of Spacetime naturally suggests discretization of Hilbert Space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert Space is discrete. We give some simple examples involving qubits and the Schrodinger wavefunction, and discuss implications for quantum information and quantum gravity.Comment: 4 pages, revtex, 1 figur
Geoffrey J Gordon - One of the best experts on this subject based on the ideXlab platform.
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Hilbert Space embeddings of predictive state representations
arXiv: Learning, 2013Co-Authors: Byron Boots, Geoffrey J Gordon, Arthur GrettonAbstract:Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of observable data, statistically consistent estimates of PSR parameters can be learned efficiently by manipulating moments of observed training data. Most learning algorithms for PSRs have assumed that actions and observations are finite with low cardinality. In this paper, we generalize PSRs to infinite sets of observations and actions, using the recent concept of Hilbert Space embeddings of distributions. The essence is to represent the state as a nonparametric conditional embedding operator in a Reproducing Kernel Hilbert Space (RKHS) and leverage recent work in kernel methods to estimate, predict, and update the representation. We show that these Hilbert Space embeddings of PSRs are able to gracefully handle continuous actions and observations, and that our learned models outperform competing system identification algorithms on several prediction benchmarks.
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UAI - Hilbert Space embeddings of predictive state representations
2013Co-Authors: Byron Boots, Arthur Gretton, Geoffrey J GordonAbstract:Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of observable data, statistically consistent estimates of PSR parameters can be learned efficiently by manipulating moments of observed training data. Most learning algorithms for PSRs have assumed that actions and observations are finite with low cardinality. In this paper, we generalize PSRs to infinite sets of observations and actions, using the recent concept of Hilbert Space embed-dings of distributions. The essence is to represent the state as one or more nonparametric conditional embedding operators in a Reproducing Kernel Hilbert Space (RKHS) and leverage recent work in kernel methods to estimate, predict, and update the representation. We show that these Hilbert Space embeddings of PSRs are able to gracefully handle continuous actions and observations, and that our learned models outperform competing system identification algorithms on several prediction benchmarks.
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Hilbert Space embeddings of predictive state representations
Uncertainty in Artificial Intelligence, 2013Co-Authors: Byron Boots, Arthur Gretton, Geoffrey J GordonAbstract:Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of observable data, statistically consistent estimates of PSR parameters can be learned efficiently by manipulating moments of observed training data. Most learning algorithms for PSRs have assumed that actions and observations are finite with low cardinality. In this paper, we generalize PSRs to infinite sets of observations and actions, using the recent concept of Hilbert Space embed-dings of distributions. The essence is to represent the state as one or more nonparametric conditional embedding operators in a Reproducing Kernel Hilbert Space (RKHS) and leverage recent work in kernel methods to estimate, predict, and update the representation. We show that these Hilbert Space embeddings of PSRs are able to gracefully handle continuous actions and observations, and that our learned models outperform competing system identification algorithms on several prediction benchmarks.
