Dynamical chiral symmetry breaking on the light front: DLCQ approach

Itakura, Kazunori; Maedan, Shinji

doi:10.1103/physrevd.61.045009

Cited by 15 publications

(97 citation statements)

References 39 publications

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“…The difficulty of describing massless particles is intimately connected with the fact that on the LF, the (massless) Nambu-Goldstone boson becomes physically meaningful only when we first include explicit breaking term and then take the vanishing limit of it [12]. The same situation was observed in the chiral Yukawa model [4].…”

Section: Introductionmentioning

confidence: 85%

“…The procedure of Ref. [4] is as follows: First, we formally solved the fermionic constraint (2.18) and substitute the solution into the zero-mode constraints (2.17). Second, we solved the zero-mode constraints by 1/N expansion with a fixed operator ordering and found that the leading order of the scalar zero-mode constraint can be identified with the gap equation.…”

Section: Implication Of the Fermionic Constraintmentioning

confidence: 99%

“…In many publications discussing the zero-mode constraints, people often choose the Weyl ordering with respect to both constrained and unconstrained variables. However, in a previous paper [4], we discussed that the ideal situation was to find a "consistent" operator ordering. For example, let us consider an anticommutator {χ, ψ} in the NJL model.…”

Section: A Quantization and The Operator Orderingmentioning

confidence: 99%

“…Therefore, in Ref. [4], we succeeded in describing indirectly the chiral symmetry breaking of the NJL model on the LF.…”

Section: Introductionmentioning

confidence: 99%

“…The explicit form of the Lagrangian in the two-component representation is given in Appendix A. In the previous work [4], we made the longitudinal direction finite in order to carefully treat the longitudinal zero modes of the scalar fields. However, in the present analysis, we work in an infinite longitudinal space.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical chiral symmetry breaking on the light front. II. The Nambu–Jona-Lasinio model

Itakura

Maedan

2000

Phys. Rev. D

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An investigation of dynamical chiral symmetry breaking on the light front is made in the NambuJona-Lasinio model with one flavor and N colors. Analysis of the model suffers from extraordinary complexity due to the existence of a "fermionic constraint," i.e., a constraint equation for the bad spinor component. However, to solve this constraint is of special importance. In classical theory, we can exactly solve it and then explicitly check the property of "light-front chiral transformation." In quantum theory, we introduce a bilocal formulation to solve the fermionic constraint by the 1/N expansion. Systematic 1/N expansion of the fermion bilocal operator is realized by the boson expansion method. The leading (bilocal) fermionic constraint becomes a gap equation for a chiral condensate and thus if we choose a nontrivial solution of the gap equation, we are in the broken phase. As a result of the nonzero chiral condensate, we find unusual chiral transformation of fields and nonvanishing of the light-front chiral charge. A leading order eigenvalue equation for a single bosonic state is equivalent to a leading order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wavefunctions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.

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Section: Introductionmentioning

confidence: 85%

Section: Implication Of the Fermionic Constraintmentioning

confidence: 99%

Section: A Quantization and The Operator Orderingmentioning

confidence: 99%

“…Therefore, in Ref. [4], we succeeded in describing indirectly the chiral symmetry breaking of the NJL model on the LF.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical chiral symmetry breaking on the light front. II. The Nambu–Jona-Lasinio model

Itakura

Maedan

2000

Phys. Rev. D

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Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

114

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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Vector mesons on the light front

2004

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We apply the light-front quantization to the Nambu-Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and pseudo-scalar mesons, we derive the bound-state equations of a qq system in the vector channel. We include the lowest order effects of the vector interaction. The resulting transverse and longitudinal components of the bound-state equation look different from each other. But eventually after imposing an appropriate cutoff, one finds these two are identical, giving the same mass and the same (spin-independent) light-cone wavefunction. Mass of the vector meson decreases as one increases the strength of the vector interaction.

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Dynamical chiral symmetry breaking on the light front: DLCQ approach

Cited by 15 publications

References 39 publications

Dynamical chiral symmetry breaking on the light front. II. The Nambu–Jona-Lasinio model

Dynamical chiral symmetry breaking on the light front. II. The Nambu–Jona-Lasinio model

Light-Cone Quantization: Foundations and Applications

Vector mesons on the light front

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