arXiv subjects

J. R. Hiller

Publications and source records attributed to J. R. Hiller.

At least 19 recordsLinked to original sources

arXiv2025

Zero Modes on the Light Front

Modes with zero longitudinal light-front momentum (zero modes) do have roles to play in the analysis of light-front field theories. These range from improvements in convergence for numerical calculations to implications for the light-front vacuum and beyond to fundamental issues in the connection with equal-time quantization. In particular, the discrepancy in values of the critical coupling for $ϕ^4_{1+1}$ theory, between equal-time and light-front quantizations, would appear to be resolvable with the proper treatment of zero modes and near-zero modes. We provide a survey of these issues and point to open questions.

hep-th↗

arXiv2024

Schrodinger-Newton solitons with axial symmetry

We solve the Schrödinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the probability density of the scalar. Unlike related calculations for condensates of ultralight dark matter or boson stars, no assumption of spherical symmetry is made for the effective gravitational potential. Instead, the potential has only axial symmetry, consistent with the axial symmetry of the particle's probability density for eigenstates of $L_z$. With total angular momentum no longer a good quantum number, there are in general contributions from a range of partial waves. This permits us to study the partial-wave content of self-consistent solutions of the Schrödinger-Newton system.

hep-th↗

arXiv2023

Effective potential between static sources in quenched light-front Yukawa theory

We compute a nonperturbative effective potential between two static fermions in light-front Yukawa theory as a Hamiltonian eigenvalue problem. Fermion pair production is suppressed, to make possible an exact analytic solution in the form of a coherent state of bosons that form clouds around the sources. The effective potential is essentially an interference term between individual clouds. The model is regulated with Pauli-Villars bosons and fermions, to achieve consistent quantization and renormalization of masses and couplings. This extends earlier work on scalar Yukawa theory where Pauli-Villars regularization did not play a central role. The key result is that the nonperturbative solution restores rotational symmetry even though the light-front formulation of Yukawa theory, with its preferred axis, appears antithetical to such a symmetry.

hep-ph↗

arXiv2023

Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations

We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schrödinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution. A static, spherically symmetric metric is computed from the field equations of general relativity, both directly and as modeled by a perfect-fluid assumption that uses the Tolman-Oppenheimer-Volkov equation for hydrostatic equilibrium of the mass density. The latter is appropriate for a Hartree approximation to the many-body problem of a bosonic star. Simultaneous self-consistent solution of the Klein--Gordon equation in this curved spacetime then yields solitons with a range of radial excitations. We compare results with the nonrelativistic case.

hep-th↗

arXiv2023

Reduced nuclear helicity amplitudes for deuteron electrodisintegration and other processes

We extend the original idea of reduced nuclear amplitudes to capture individual helicity amplitudes and discuss various applications to exclusive processes involving the deuteron. Specifically, we consider deuteron form factors, structure functions, tensor polarization observables, photodisintegration, and electrodisintegration. The basic premise is that nuclear processes at high momentum transfer can be approximated by tree graphs for point-like nucleons supplemented by empirical form factors for each nucleon. The latter represent the internal structure of the nucleon, and incorporate nonperturbative physics, which can allow for early onset of scaling behavior. The nucleon form factors are evaluated at the net momentum transfer experienced by the given nucleon, with use of $G_E$ for a no-flip contribution and $G_M$ for a helicity-flip contribution. Results are compared with data where available. The deuteron photodisintegration asymmetry $Σ$ is obtained with a value of $Σ(90^\circ)\simeq -0.06$, which is much closer to experiment than the value of -1 originally expected. The method also provides an estimate of the momentum transfer values required for scaling onset. We find that the deuteron structure function $B$ is a good place to look, above momentum transfers of 10 GeV$^2$.

nucl-th↗

arXiv2020

Casimir force on a light front

Depending on the point of view, the Casimir force arises from variation in the energy of the quantum vacuum as boundary conditions are altered or as an interaction between atoms in the materials that form these boundary conditions. Standard analyses of such configurations are usually done in terms of ordinary, equal-time (Minkowski) coordinates. However, physics is independent of the coordinate choice, and an analysis based on light-front coordinates, where $x^+\equiv t+z/c$ plays the role of time, is equally valid. After a brief historical introduction, we illustrate and compare equal-time and light-front calculations of the Casimir force.

hep-th↗

arXiv2017

Klein-Gordon equation in curved space-time

We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere with a linear transition from constant to zero density; in each case the radius of the central mass is chosen to be sufficient to avoid any event horizon. The solutions are obtained numerically and compared with nonrelativistic Coulomb-type solutions, both directly and in perturbation theory, to study the general-relativistic corrections to the quantum solutions for a $1/r$ potential. The density profile with a linear transition is chosen to avoid singularities in the wave equation that can be caused by a discontinuous derivative of the density.

gr-qc↗

arXiv2016

Light-front $ϕ_2^4$ theory with sector-dependent mass

As an extension of recent work on two-dimensional light-front $ϕ^4$ theory, we implement Fock-sector dependence for the bare mass. Such dependence should have important consequences for the convergence of nonperturbative calculations with respect to the level of Fock-space truncation. The truncation forces the self-energy corrections to be sector-dependent; in particular, the highest sector has no self-energy correction. Thus, the bare mass can be considered sector dependent as well. We find that, although higher Fock sectors have a larger probability, the mass of the lightest state and the value of the critical coupling are not significantly affected. This implies that coherent states or the light-front coupled-cluster method may be required to properly represent critical behavior.

hep-th↗

arXiv2016

Symmetry breaking in light-front $ϕ^4$ theory

We consider the symmetric and broken phases of light-front $ϕ^4$ theory in two dimensions. In both cases the mass of the lowest state is computed and its dependence on the coupling used to infer critical coupling values. The structure of the eigenstate is examined to determine whether it shows the signs of critical behavior, specifically whether the one-body sector becomes improbable relative to the higher Fock sectors. In attempts to establish this behavior, we consider both sector-independent and sector-dependent constituent masses.

hep-th↗

arXiv2016

Two-dimensional light-front $ϕ^4$ theory in a symmetric polynomial basis

We study the lowest-mass eigenstates of $ϕ^4_{1+1}$ theory with both odd and even numbers of constituents. The calculation is carried out as a diagonalization of the light-front Hamiltonian in a Fock-space representation. In each Fock sector a fully symmetric polynomial basis is used to represent the Fock wave function. Convergence is investigated with respect to the number of basis polynomials in each sector and with respect to the number of sectors. The dependence of the spectrum on the coupling strength is used to estimate the critical coupling for the positive-mass-squared case. An apparent discrepancy with equal-time calculations of the critical coupling is resolved by an appropriate mass renormalization.

hep-th↗

arXiv2016

Nonperturbative light-front Hamiltonian methods

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli--Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, $ϕ^4$ theory, ordinary Yukawa theory, supersymmetric Yang--Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

hep-ph↗

arXiv2015

Pauli-Villars regularization of non-Abelian gauge theories

As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev--Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.

hep-th↗

arXiv2014

The Casimir effect in light-front quantization

We show that the standard result for the Casimir force between conducting plates at rest in an inertial frame can be computed in light-front quantization. This is not the same as light-front analyses where the plates are at "rest" in an infinite momentum frame. In that case, Lenz and Steinbacher have shown that the result does not agree with the standard result for plates at rest. The two important ingredients in the present analysis are a careful treatment of the boundary conditions, inspired by the work of Almeida et al. on oblique light-front coordinates, and computation of the ordinary energy density, rather than the light-front energy density.

hep-th↗

arXiv2014

Basis of symmetric polynomials for many-boson light-front wave functions

We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the coordinates is one. These polynomials form a basis for the expansion of bosonic light-front momentum-space wave functions, as functions of longitudinal momentum, where momentum conservation guarantees that the fractions are on the interval $[0,1]$ and sum to one. This generalizes earlier work on three-boson wave functions to wave functions for arbitrarily many identical bosons. A simple application in two-dimensional $ϕ^4$ theory illustrates the use of these polynomials.

hep-ph↗

arXiv2014

Application of the light-front coupled-cluster method to $ϕ^4$ theory in two dimensions

As a first numerical application of the light-front coupled-cluster (LFCC) method, we consider the odd-parity massive eigenstate of $ϕ_{1+1}^4$ theory. The eigenstate is built as a Fock-state expansion in light-front quantization, where wave functions appear as coefficients of the Fock states. A standard Fock-space truncation would then yield a finite set of linear equations for a finite number of wave functions. The LFCC method replaces Fock-space truncation with a more sophisticated truncation, one which reduces the eigenvalue problem to a finite set of nonlinear equations without any restriction on Fock space. We compare our results with those obtained with a Fock-space truncation that yields the same number of equations.

hep-ph↗

arXiv2014

Light-front holography and the light-front coupled-cluster method

We summarize the light-front coupled-cluster (LFCC) method for the solution of field-theoretic bound-state eigenvalue problems and indicate the connection with light-front holographic QCD. This includes a sample application of the LFCC method and leads to a relativistic quark model for mesons that adds longitudinal dynamics to the usual transverse light-front holographic Schrodinger equation.

hep-ph↗

arXiv2013

Zero modes in the light-front coupled-cluster method

The light-front coupled-cluster (LFCC) method is a technique for solving Hamiltonian eigenvalue problems in light-front-quantized field theories. Its primary purpose is to provide a systematic sequence of solvable approximations to the original eigenvalue problem without the truncation of Fock space. Here we discuss the incorporation of zero modes, modes of zero longitudinal momentum, into the formalism of the method. Without zero modes, the light-front vacuum is trivial, and the vacuum expectation value of the field is always zero. The LFCC method with zero modes provides for vacuum structure, in the form of a generalized coherent state of zero modes, as is illustrated here in two-dimensional model field theories.

hep-ph↗

arXiv2013

Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics

An 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 lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties.

hep-ph↗