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Causal Inference in Higher Education: Building Better CurriculumsJun 11 2019Higher educational institutions constantly look for ways to meet students' needs and support them through graduation. Recent work in the field of learning analytics have developed methods for grade prediction and course recommendations. Although these ... More

Relativistic few-body physicsDec 12 2013I discuss different formulations of the relativistic few-body problem with an emphasis on how they are related. I first discuss the implications of some of the differences with non-relativistic quantum mechanics. Then I point out that the principle of ... More

Relativistic few-body methodsSep 03 2015I discuss the role of relativistic quantum mechanics in few-body physics, various formulations of relativistic few-body quantum mechanics and how they are related.

Power countings versus physical scalings in disordered elastic systems - Case study of the one-dimensional interfaceOct 05 2016We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical fluctuations as a ... More

Nontrivial rheological exponents in sheared yield stress fluidsFeb 10 2016May 08 2016We discuss possible physical origins for non-trivial exponents in the flow behaviour of athermally yielding soft materials at intermediate shear rates. Studying analytically a mean-field model that describes the mechanical noise through a diffusion term ... More

Progress in Euclidean relativistic few-body quantum mechanicsOct 07 2012We discuss recent progress in the Euclidean formulation of relativistic few-body quantum mechanics.

Relativistic Quantum Mechanics - Particle Production and Cluster PropertiesFeb 11 2003This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a bounded number ... More

Cluster properties and particle production in Poincaré invariant quantum mechanicsJan 26 2010I outline the construction of exactly Poincar\'e invariant quantum models that satisfy cluster separability but do not conserve particle number.

Equivalent HamiltoniansJan 25 2010Aug 31 2010I give a characterization of the conditions for two Hamiltonians to be equivalent, discuss the construction of the operators that relate equivalent Hamiltonians, and introduce variational methods that can select Hamiltonians with desirable features from ... More

Representations of relativistic particles of arbitrary spin in Poincaré, Lorentz, and Euclidean covariant formulations of relativistic quantum mechanicsSep 25 2018Jan 16 2019Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current matrix elements ... More

Computational challenges in the relativistic few-nucleon problemDec 12 2013I discuss computational challenges in the relativistic few-nucleon problem and the resolution of some of these challenges. I also discuss the outlook for the future.

Cluster properties in relativistic quantum mechanics of N-particle systemsJan 07 2002May 30 2003A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincar\'e invariance, cluster separability, and the spectral condition. Irreducible representations and Clebsch-Gordan coefficients ... More

A Theorem on Light-Front Quantum ModelsMay 18 1993I give a sufficient condition for a relativistic front-form quantum mechanical model to be scattering equivalent (unitarily equivalent with the same S-matrix elements) to a relativistic front-form quantum model with an interaction-independent front-form ... More

A Euclidean formulation of relativistic quantum mechanicsJun 21 2011In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert ... More

Poincaré invariant quantum theory, J. Lab lecturesAug 11 2009Lectures on Poincare invariant quantum theory presented at TJNAF.

Poincare Invariance, Cluster Properties, and Particle ProductionNov 07 2002A method is presented for constructing a class of Poincare invariant quantum mechanical models of systems of a finite number of degrees of freedom that satisfy cluster separability, the spectral condition, but do not conserve particle number. The class ... More

Euclidean Relativistic Quantum MechanicsJan 28 2013We discuss a formulation of exactly Poincar\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the construction ... More

The light-front vacuumJan 08 2016We discuss the relation between the trivial light-front vacuum and the non-trivial Heisenberg vacuum.

The light-front vacuum and dynamicsSep 22 2004I give a quantum theoretical description of kinematically invariant vacuua on the algebra of free fields restricted to a light front and discuss the relation between the light-front Hamiltonian, P-, the vacuum, and Poincare invariance. This provides a ... More

Nucleon-Nucleon Interactions and ObservablesNov 24 1997A class of nucleon-nucleon interactions which are exactly phase equivalent to a given realistic nucleon-nucleon interaction are exhibited. These interaction have the property that the RMS radius of the deuteron can be made arbitrarily large without changing ... More

Vacuum Structures in Hamiltonian Light-Front DynamicsMay 10 1993Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which ... More

Scattering and reflection positivity in relativistic Euclidean quantum mechanicsDec 12 2013Apr 22 2014In this paper I discuss a formulation of relativistic few-particle scattering theory where the dynamical input is a collection of reflection-positive Euclidean covariant Green functions. This formulation of relativistic quantum mechanics has the advantage ... More

Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamicsAug 31 2010We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of proving that ... More

Cluster Properties and Particle Production in Relativistic Quantum MechanicsAug 22 2003I formulate a class of relativistic quantum mechanical models that satisfy the cluster property and allow particle production. The models have a finite number of bare-particle degrees of freedom. The class of models include relativistic isobar models ... More

The Light-Front VacuumFeb 04 2015Background: The vacuum in the light-front representation of quantum field theory is trivial while vacuum in the equivalent canonical representation of the same theory is non-trivial. Purpose: Understand the relation between the vacuum in light-front and ... More

Scattering asymptotic conditions in Euclidean relativistic quantum theoryDec 10 2015We discuss the formulation of the scattering asymptotic condition as a strong limit in Euclidean quantum theories satisfying the Osterwalder-Schrader axioms. When used with the invariance principle this provides a constructive method to compute scattering ... More

Stability of Covariant Relativistic Quantum TheoryDec 01 2003May 31 2004In this paper we study the relativistic quantum mechanical interpretation of the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal is to determine conditions on the input to the Euclidean Bethe-Salpeter equation so the solution ... More

Wavelets in field theoryDec 12 2013We discuss the use of Daubechies wavelets in discretizing quantum field theories.

Disordered Elastic Systems and One-Dimensional InterfacesNov 21 2011We briefly introduce the generic framework of Disordered Elastic Systems (DES), giving a short `recipe' of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems. ... More

Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation: numerical studyMay 10 2013We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi>0$, and at finite temperature ... More

Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strainMar 29 2019As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in $d$ dimensions, submitted to an external shear strain. ... More

Relativistic Quantum Dynamics of Many-Body SystemsFeb 22 2001Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract framework of ... More

Charge Form Factors of Quark-Model Pions IIMay 30 2004Sep 20 2004Experimental data of the pion charge form factor are well represented by Poincar\'e invariant constituent-quark phenomenology depending on two parameters, a confinement scale and an effective constituent--quark mass. Pion states are represented by eigenfunctions ... More

A momentum-space Argonne V18 interactionJun 10 2011This paper gives a momentum-space representation of the Argonne V18 potential as an expansion in products of spin-isospin operators with scalar coefficient functions of the momentum transfer. Two representations of the scalar coefficient functions for ... More

Exchange current contributions in null-plane quantum models of elastic electron deuteron scatteringDec 11 2008Aug 09 2009We investigate exchange current contributions to elastic electron-deuteron scattering using exactly Poincar\'e invariant quantum mechanics with a null-plane kinematic symmetry. Our model exchange current is motivated by one-pion-exchange physics. Exact ... More

Euclidean formulation of relativistic quantum mechanicsAug 10 2009We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare invariant S-matrix ... More

Wavelets in Field TheoryJan 28 2013Jun 05 2013We advocate the use of Daubechies wavelets as a basis for treating a variety of problems in quantum field theory. This basis has both natural large volume and short distance cutoffs, has natural partitions of unity, and the basis functions are all related ... More

Temperature-induced crossovers in the static roughness of a one-dimensional interfaceAug 20 2010At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian Variational Method (GVM), we explore the consequences of ... More

Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulationSep 04 2012May 13 2013Experimental realizations of a 1D interface always exhibit a finite microscopic width $\xi>0$; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description of the interface ... More

Pointlike constituent quarks and scattering equivalencesJun 15 2004Jun 23 2004In this paper scattering equivalences are used to simplify current operators in constituent quark models. The simplicity of the method is illustrated by applying it to a relativistic constituent quark model that fits the meson mass spectrum. This model ... More

Euclidean relativistic quantum mechanics - scattering asymptotic conditionsNov 11 2016We discuss the formulation of the scattering asymptotic condition in a relativistic quantum theory formulated in terms of reflection positive Euclidean Green functions.

Wavelet Methods in the Relativistic Three-Body ProblemJul 22 2005Jul 30 2005In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This ... More

Constraints of cluster separability and covariance on current operatorsOct 06 2011Realistic models of hadronic systems should be defined by a dynamical unitary representation of the Poincare group that is also consistent with cluster properties and a spectral condition. All three of these requirements constrain the structure of the ... More

Poincaré Invariant Quantum Mechanics based on Euclidean Green functionsAug 31 2010We investigate a formulation of Poincar\'e invariant quantum mechanics where the dynamical input is Euclidean invariant Green functions or their generating functional. We argue that within this framework it is possible to calculate scattering observables, ... More

Relativistic Formulation of Reaction TheoryApr 09 2014Jun 06 2014A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincar\'e group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles to which rotationally ... More

Multiscaling analysis of ferroelectric domain wall roughnessMay 01 2012Oct 09 2012Using multiscaling analysis, we compare the characteristic roughening of ferroelectric domain walls in PZT thin films with numerical simulations of weakly pinned one-dimensional interfaces. Although at length scales up to a length scale greater or equal ... More

Flow equations and wavelet truncationsOct 27 2016We investigate both theoretical and computational aspects of using wavelet bases to decouple physics on different scales in quantum field theory.

Spin and dynamics in relativistic quantum theoriesOct 02 2014The role of relativity and dynamics in defining the spin and orbital angular momentum content of hadronic systems is discussed.

Relativistic quantum theories and neutrino oscillationsAug 10 2009Apr 15 2010Neutrino oscillations are examined under the broad requirements of Poincar\'e-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The goal of this ... More

Cluster properties in Poincare invariant quantum mechanicsOct 05 2012Using a simple model we provide a quantitative study of the size of the corrections needed to restore cluster properties to the construction of Poincare invariant dynamical models with kinematic spins, first provided by B. Bakamjian and L. H. Thomas. ... More

Model tests of cluster separability in relativistic quantum mechanicsSep 29 2011Jul 05 2012A relativistically invariant quantum theory first advanced by Bakamjian and Thomas has proven very useful in modeling few-body systems. For three particles or more, this approach is known formally to fail the constraint of cluster separability, whereby ... More

KPZ equation with correlated noise: emergent symmetries and non-universal observablesNov 07 2016We investigate the steady-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional Renormalization Group ... More

Useful Bases for Problems in Nuclear and Particle PhysicsNov 25 1996A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be exactly ... More

Two-Nucleon Scattering without partial waves using a momentum space Argonne V18 interactionJun 21 2012Jul 19 2012We test the operator form of the Fourier transform of the Argonne V18 potential by computing selected scattering observables and all Wolfenstein parameters for a variety of energies. These are compared to the GW-DAC database and to partial wave calculations. ... More

Multiresolution decomposition of quantum field theories using wavelet basesOct 27 2016Apr 14 2017We investigate both theoretical and computational aspects of using wavelet bases to decouple physics on different scales in quantum field theory.

Quantitative Relativistic Effects in the Three-Nucleon ProblemJul 29 2005The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations ... More

Causality in Dense MatterMay 14 1996The possibility of non-causal signal propagation is examined for various theories of dense matter. This investigation requires a discussion of definitions of causality, together with interpretations of spacetime position. Specific examples are used to ... More

Finite-temperature and finite-time scaling of the directed polymer free-energy with respect to its geometrical fluctuationsJun 28 2012We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse fluctuations of the ... More

On the relevance of disorder in athermal amorphous materials under shearJan 19 2015May 27 2015We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly ... More

Statistics of domain wall roughness: A survey of different scaling analysesApr 26 2019Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review these different ... More

Spin in relativistic quantum theoryAug 29 2012We discuss the role of spin in Poincar\'e invariant formulations of quantum mechanics.

Multi-scale methods in quantum field theoryNov 30 2017Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet ... More

Nonlinear Rheology in a Model Biological TissueNov 15 2016Apr 17 2017Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model ... More

Wavelet NotesMay 10 2003Dec 04 2003Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation of operators ... More

Comparison of Relativistic Nucleon-Nucleon InteractionsMay 23 2000Aug 02 2000We investigate the difference between those relativistic models based on interpreting a realistic nucleon-nucleon interaction as a perturbation of the square of a relativistic mass operator and those models that use the method of Kamada and Gl\"ockle ... More

Three-body scattering in Poincaré invariant quantum mechanicsNov 11 2007The relativistic three-nucleon problem is formulated by constructing a dynamical unitary representation of the Poincar\'e group on the three-nucleon Hilbert space. Two-body interactions are included that preserve the Poincar\'e symmetry, lead to the same ... More

Wavelets in Momentum-Space Scattering CalculationsAug 22 2003We demonstrate that wavelet bases have features that make them advantageous for solving momentum-space scattering integral equations. Using the example of two nucleons interacting with the Malfliet-Tjon V interaction, we show it is possible to reduce ... More

Scattering Calculations with WaveletsNov 06 2002We show that the use of wavelet bases for solving the momentum-space scattering integral equation leads to sparse matrices which can simplify the solution. Wavelet bases are applied to calculate the K-matrix for nucleon-nucleon scattering with the s-wave ... More

The Balian-Brézin Method in Relativistic Quantum MechanicsMar 16 1994The method suggested by Balian and Br\'ezin for treating angular momentum reduction in the Faddeev equations is shown to be applicable to the relativistic three-body problem.

Point-Form Analysis of Elastic Deuteron Form FactorsMay 17 2000Oct 11 2000Point-form relativistic quantum mechanics is applied to elastic electron-deuteron scattering. The deuteron is modeled using relativistic interactions that are scattering-equivalent to the nonrelativistic Argonne $v_{18}$ and Reid '93 interactions. A point-form ... More

Relativistic Three-Body Scattering in a First Order Faddeev FormulationAug 28 2007Oct 01 2007Relativistic Faddeev equations for three-body scattering at arbitrary energies are solved in first order in the two-body transition operator in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated ... More

The Relativistic Three-Body Bound State in a 3D FormulationSep 05 2014Background: The relativistic three-body problem has a long tradition in few-nucleon physics. Calculations of the triton binding energy based on the solution of the relativistic Faddeev equation in general lead to a weaker binding than the corresponding ... More

Relativistic Effects in Exclusive pd Breakup Scattering at Intermediate EnergiesOct 22 2007The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is achieved by constructing a dynamical ... More

First Order Relativistic Three-Body ScatteringFeb 01 2007Jun 25 2007Relativistic Faddeev equations for three-body scattering at arbitrary energies are formulated in momentum space and in first order in the two-body transition-operator directly solved in terms of momentum vectors without employing a partial wave decomposition. ... More

Non-linear rheology in a model biological tissueNov 15 2016Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model ... More

Application of wavelets to singular integral scattering equationsJun 28 2004The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties ... More

The Relativistic Three-Body Bound State in Three-DimensionsAug 20 2015Studying of the relativistic three-body bound state in a three-dimensional (3D) approach is a necessary first step in a process to eventually perform scattering calculations at GeV energies, where partial-wave expansions are not useful. To this aim we ... More

Poincare Invariant Three-Body ScatteringDec 10 2008Relativistic Faddeev equations for three-body scattering are solved at arbitrary energies in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated withing the framework of Poincar\'e invariant ... More

Driven interfaces: from flow to creep through model reductionMay 14 2016Jul 28 2016The response of spatially extended systems to a force leading their steady state out of equilibrium is strongly affected by the presence of disorder. We focus on the mean velocity induced by a constant force applied on one-dimensional interfaces. In the ... More

Relativity and the low energy nd Ay puzzleJan 02 2008We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. ... More

Lorentz Boosted Nucleon-Nucleon T-matrix and the Triton Binding EnergyOct 13 2008The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, ... More

Three-nucleon force in relativistic three-nucleon Faddeev calculationsJan 21 2011Feb 16 2011We extend our formulation of relativistic three-nucleon Faddeev equations to include both pairwise interactions and a three-nucleon force. Exact Poincare invariance is realized by adding interactions to the mass Casimir operator (rest Hamiltonian) of ... More

Poincaré Invariant Three-Body Scattering at Intermediate EnergiesJan 21 2008The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. The equation is solved through Pad\'e summation, and the numerical ... More

Mini review of Poincaré invariant quantum theoryAug 31 2010We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert spaces, the ... More

A Poincaré invariant treatment of the three-nucleon problemDec 11 2008I summarize recent progress in the treatment of the Poincar\'e three-nucleon problem at intermediate energies

Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physicsSep 24 2013An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established ... More