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S. S. Chabysheva

Publications and source records attributed to S. S. Chabysheva.

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

Light-front versus equal-time quantization in $ϕ^4$ theory

There is a discrepancy between light-front and equal-time values for the critical coupling of two-dimensional $ϕ^4$ theory. A proposed resolution is to take into account the difference between mass renormalizations in the two quantizations. This distinction was first discussed by M. Burkardt. It prevents direct comparison of bare parameters; however, a method proposed here allows calculation of the difference and thereby resolves the discrepancy. We also consider the consequences of allowing a sector-dependent constituent mass.

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↗
arXiv2015

Light-front $ϕ^4_{1+1}$ theory using a many-boson symmetric-polynomial basis

We extend earlier work on fully symmetric polynomials for three-boson wave functions to arbitrarily many bosons and apply these to a light-front analysis of the low-mass eigenstates of $ϕ^4$ theory in 1+1 dimensions. The basis-function approach allows the resolution in each Fock sector to be independently optimized, which can be more efficient than the preset discrete Fock states in DLCQ. We obtain an estimate of the critical coupling for symmetry breaking in the positive mass-squared case.

hep-ph↗
arXiv2014

The light-front coupled-cluster method applied to $ϕ_{1+1}^4$ theory

We use the light-front coupled-cluster (LFCC) method to compute the odd-parity massive eigenstate of $ϕ_{1+1}^4$ theory. A standard Fock-space truncation of the eigenstate yields 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; the eigenvalue problem is reduced to a finite set of nonlinear equations without any restriction on Fock space, but with restrictions on the Fock wave functions. We compare our results with those obtained with a Fock-space truncation.

hep-ph↗
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↗
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

A dynamical model for longitudinal wave functions in light-front holographic QCD

We construct a Schrodinger-like equation for the longitudinal wave function of a meson in the valence qq-bar sector, based on the 't Hooft model for large-N two-dimensional QCD, and combine this with the usual transverse equation from light-front holographic QCD, to obtain a model for mesons with massive quarks. The computed wave functions are compared with the wave function ansatz of Brodsky and De Teramond and used to compute decay constants and parton distribution functions. The basis functions used to solve the longitudinal equation may be useful for more general calculations of meson states in QCD.

hep-ph↗
arXiv2012

An illustration of the light-front coupled-cluster method in quantum electrodynamics

A field-theoretic formulation of the exponential-operator technique is applied to a nonperturbative Hamiltonian eigenvalue problem in electrodynamics, quantized in light-front coordinates. Specifically, we consider the dressed-electron state, without positron contributions but with an unlimited number of photons, and compute its anomalous magnetic moment. A simple perturbative solution immediately yields the Schwinger result of α/2π. The nonperturbative solution, which requires numerical techniques, sums a subset of corrections to all orders in α and incorporates additional physics.

hep-ph↗