RECORD
Light-Cone Quantization: Foundations and Applications
High Energy Physics - Theory · Submitted 11 Aug 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, the triviality of the light-cone vacuum is established.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
These lecture notes review the foundations and some applications of light-cone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincare 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 Schroedinger 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 Schroedinger 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 Schroedinger 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | These lecture notes review the foundations and some applications of light-cone quantization. | contribution 0.64 | 0.31 | 0.04 | asserted 0.92 |
| s1 | First I explain how to choose a time in special relativity. | background 0.52 | 0.50 | 0.02 | asserted 0.76 |
| s2 | Inclusion of Poincare invariance naturally leads to Dirac's forms of relativistic dynamics. | background 0.98 | 0.11 | 0.03 | asserted 1.00 |
| s3 | Among these, the front form, being the basis for light-cone quantization, is my main focus. | background 0.51 | 0.33 | 0.05 | asserted 0.98 |
| s4 | I explain a few of its peculiar features such as boost and Galilei invariance or separation of relative and center-of-mass motion. | contribution 0.61 | 0.47 | 0.02 | asserted 0.94 |
| s5 | Combining light-cone dynamics and field quantization results in light-cone quantum field theory. | background 0.65 | 0.19 | 0.04 | asserted 1.00 |
| s6 | As the latter represents a first-order system, quantization is somewhat nonstandard. | background 0.93 | 0.13 | 0.03 | asserted 0.79 |
| s7 | I address this issue using Schwinger's quantum action principle, the method of Faddeev and Jackiw, and the functional Schroedinger picture. | method 0.96 | 0.67 | 0.03 | asserted 0.99 |
| s8 | A finite-volume formulation, discretized light-cone quantization, is analysed in detail. | contribution 0.56 | 0.74 | 0.04 | asserted 0.99 |
| s9 | I point out some problems with causality, which are absent in infinite volume. | limitation 0.69 | 0.67 | 0.04 | asserted 0.99 |
| s10 | Finally, the triviality of the light-cone vacuum is established. | result 0.92 | 0.81 | 0.14 | asserted 1.00 |
| s11 | Coming to applications, I introduce the notion of light-cone wave functions as the solutions of the light-cone Schroedinger equation. | method 0.50 | 0.60 | 0.04 | asserted 0.99 |
| s12 | I discuss some examples, among them nonrelativistic Coulomb systems and model field theories in two dimensions. | contribution 0.92 | 0.68 | 0.02 | asserted 0.91 |
| s13 | Vacuum properties (like chiral condensates) are reconstructed from the particle spectrum obtained by solving the light-cone Schroedinger equation. | result 0.67 | 0.71 | 0.08 | asserted 1.00 |
| s14 | In a last application, I make contact with phenomenology by calculating the pion wave function within the Nambu and Jona-Lasinio model. | contribution 0.75 | 0.90 | 0.05 | asserted 0.97 |
| s15 | 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. | result 0.93 | 0.92 | 0.18 | asserted 0.99 |
| s16 | The latter turns out to be the asymptotic one. | result 0.95 | 0.85 | 0.12 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
These lecture notes review the foundations and some applications of light-cone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincare 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 Schroedinger 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 Schroedinger 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 Schroedinger 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.
Human review
References
How the literature uses it
39 arXiv papers cite this in 57 sentences
Papers citing it · 39 sentences without a confident label
Uses its method or tool 2 papers
-
We use the residue theorem, but because of the dependence of the background on $x^$, the integrals are performed as in lightfront field theory [ref] .
Gluon helicity flip in a plane wave background · Ghost loop · 0.99
-
In light-front coordinates one can integrate by parts to find (the surface terms cancel against $S_bdy$) [equation] We adopt $$ as light-front time [ref] and read off the Poisson bracket [ref] [equation] $A_+$ is a Lagrange multiplier that enforces the Chern-Simons Gauss law.
Holographic representation of bulk fields with spin in AdS/CFT · Chern-Simons in holographic gauge · 0.92
Compares with it 1 paper
-
The result ([ref]) coincides with the light-front vacuum wave functional for free scalar fields found in [ref] .
Noncommutativity from spectral flow · Light-front limit of wave functionals - the vacuum · 0.99
Cites it as support 2 papers
-
Work on the light-front canonical analysis shows that a distributional Dirac bracket like [ref] is obtained under trivial or periodic boundary conditions [ref] , both incompatible with memory.
An algebra of proper observables at null infinity: Dirac brackets, Memory and Goldstone probes · Introduction · 0.96
-
Second, all (matter particle) number-changing terms drop out of the Hamiltonian due to longitudinal momentum conservation [ref] , hence the different $n$-particle sectors of Fock space are decoupled automatically.
Mode truncations and scattering in strong fields · Front form quantisation with zero modes · 0.97
Cites it as background 13 papers
-
These `zero mode' singularities are well known from lightfront field theory, reviewed in e.g. [ref] , where they have a long history and are intrinsically linked to the structure of the vacuum [ref] .
Very Special Relativity as a background field theory · Lightfront gauge · 0.91
-
Light-front quantization and the associated light-front wave functions (LFWFs) provide a powerful framework with which to study quantum chromodynamics (QCD) and develop an understanding of the parton structure of hadrons [ref] .
Intrinsic Transverse Motion of the Pion's Valence Quarks · Introduction · 0.99
-
In the light-front formalism, field theories are quantised at fixed light-front time $x^=x^0+x^3$, following [ref] , rather than at fixed $x^0$ as in the equal-time formalism; see [ref] for reviews.
Scattering in strong electromagnetic fields: transverse size effects in tBLFQ · Background · 0.94
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.