A light-front coupled-cluster method for the nonperturbative solution of quantum field theories

Chabysheva, Sophia S.; Hiller, John R.

doi:10.1016/j.physletb.2012.04.032

Cited by 46 publications

(66 citation statements)

References 41 publications

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“…The LFCC method [21] avoids the difficulties associated with an explicit Fock-space truncation by truncating the set of coupled equations in a very different way. Instead of truncating the number of particles, it truncates the way in which wave functions are related to each other; the wave functions of higher Fock states are determined by the lower-state wave functions and the exponentiation of an operator T .…”

Section: Light-front Coupled-cluster Methodsmentioning

confidence: 99%

“…This can lead to inconsistencies in the interpretation of the wave functions [20]. The other solution is the light-front coupled-cluster (LFCC) method [21], in which the truncation is in the way that higher Fock-state wave functions are related to the lower wave functions, with no Fock-space truncation. In either case, the bare parameters are fixed by fitting observables.…”

Section: Introductionmentioning

confidence: 99%

“…This is followed by Sec. 3 on the various methods used for light-front calculations, from the original discretized light-cone quantization (DLCQ) [12], including its supersymmetric extension, SDLCQ [33], to function expansion methods [14,34], the LFCC method [21], and the effective particle approach [29]. The third main section, Sec.…”

Section: Introductionmentioning

confidence: 99%

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Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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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.

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Section: Light-front Coupled-cluster Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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“…A related approach for determining the valence light-front wavefunction and studying the effects of higher Fock states without truncation has been given in Ref. [90].…”

Section: Azimuthal Basis ζϕmentioning

confidence: 99%

QCD on the Light-Front

2013

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Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x + = x 0 + x 3 , provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian HLF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of HLF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable ζ 2 = b 2 ⊥ x(1−x), which is conjugate to the invariant mass squared M 2 qq . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories M 2 (n, L, S) = 4κ 2 (n+L+S/2) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.

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“…However, the truncation induces various complications, not the least of which are uncanceled divergences and Fock-sector dependencies [3]. The light-front coupled-cluster (LFCC) method [4] avoids these complications by not truncating Fock space and instead approximating the relationship between wave functions to obtain a finite set of equations for a still infinite collection of wave functions. There is a price to be paid, of course; the resulting equations are nonlinear and the calculation of matrix elements requires particular care.…”

Section: Introductionmentioning

confidence: 99%

A nonperturbative coupled-cluster method for quantum field theories

Hiller

2013

AIP Conference Proceedings

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The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponentialoperator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.

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A light-front coupled-cluster method for the nonperturbative solution of quantum field theories

Cited by 46 publications

References 41 publications

Nonperturbative light-front Hamiltonian methods

Nonperturbative light-front Hamiltonian methods

QCD on the Light-Front

A nonperturbative coupled-cluster method for quantum field theories

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