Discretized light-cone quantization: Solution to a field theory in one space and one time dimension

Pauli, Hans–Christian; Brodsky, Stanley J.

doi:10.1103/physrevd.32.2001

Cited by 297 publications

(153 citation statements)

References 5 publications

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“…DLCQ is the acronym for 'discretized light-cone quantization', originally developed by (Maskawa and Yamawaki 1976;Pauli and Brodsky 1985a;Pauli and Brodsky 1985b) 4 . The physical system under consideration is enclosed in a finite volume with discrete momenta and prescribed boundary conditions in x − .…”

Section: Dlcq -Basicsmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

112

141

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Abstract. These lecture notes review the foundations and some applications of lightcone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincaré invariance naturally leads to Dirac's forms of relativistic dynamics. Among these, the front form, being the basis for light-cone quantization, is my main focus. I explain a few of its peculiar features such as boost and Galilei invariance or separation of relative and center-of-mass motion. Combining light-cone dynamics and field quantization results in light-cone quantum field theory. As the latter represents a first-order system, quantization is somewhat nonstandard. I address this issue using Schwinger's quantum action principle, the method of Faddeev and Jackiw, and the functional Schrödinger picture. A finite-volume formulation, discretized light-cone quantization, is analysed in detail. I point out some problems with causality, which are absent in infinite volume. Finally, the triviality of the light-cone vacuum is established. Coming to applications, I introduce the notion of light-cone wave functions as the solutions of the light-cone Schrödinger equation. I discuss some examples, among them nonrelativistic Coulomb systems and model field theories in two dimensions. Vacuum properties (like chiral condensates) are reconstructed from the particle spectrum obtained by solving the light-cone Schrödinger equation. In a last application, I make contact with phenomenology by calculating the pion wave function within the Nambu and Jona-Lasinio model. I am thus able to predict a number of observables like the pion charge and core radius, the r.m.s. transverse momentum, the pion structure function and the pion distribution amplitude. The latter turns out to be the asymptotic one.

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Section: Dlcq -Basicsmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

112

141

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“…The Hamiltonian eigenvalue problem is then transformed into a coupled set of integral equations for these wave functions, with the invariant mass of the eigenstate as the eigenvalue. As such, the approach lends itself well to numerical solution by discretization [12,2] and by basis-function expansions [13,14].…”

Section: Introductionmentioning

confidence: 99%

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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“…A time-honored technique is discrete light-cone quantization (DLCQ), which compactifies x − to get a discrete spectrum for the Hamiltonian evolution in the x þ direction [57,58]. While this idea has been around for a while (see [59] for a review), it has not yet become a viable alternative to the lattice above d ¼ 2 dimensions.…”

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confidence: 99%

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

2015

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We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the truncated conformal space approach, a Hamiltonian method which exploits the conformal structure of the UV fixed point. The theory is regulated in the IR by putting it on a sphere of a large finite radius. The quantum field theory Hamiltonian is expressed as a matrix in the Hilbert space of conformal field theory states. After restricting ourselves to energies below a certain UV cutoff, an approximation to the spectrum is obtained by numerical diagonalization of the resulting finite-dimensional matrix. The cutoff dependence of the results can be computed and efficiently reduced via a renormalization procedure. We work out the details of the method for the ϕ 4 theory in d dimensions with d being not necessarily integer. A numerical analysis is then performed for the specific case d ¼ 2.5, a value chosen in the range where UV divergences are absent. By going from weak to intermediate to strong coupling, we are able to observe the symmetry-preserving, symmetry-breaking, and conformal phases of the theory, and perform rough measurements of masses and critical exponents. As a byproduct of our investigations we find that both the free and the interacting theories in nonintegral d are not unitary, which however does not seem to cause much effect at low energies.

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Discretized light-cone quantization: Solution to a field theory in one space and one time dimension

Cited by 297 publications

References 5 publications

Light-Cone Quantization: Foundations and Applications

Light-Cone Quantization: Foundations and Applications

Nonperturbative light-front Hamiltonian methods

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

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