Relativistic model of nucleon and pion structure: Static properties and electromagnetic soft form factors

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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“…in (Dziembowski 1988;Chung et al 1988;Jaus 1990;Ji and Cotanch 1990;Ji et al 1992). The NJL wave function of the pion thus becomes…”

Section: Schwinger-dyson Approachmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Lecture Notes in Physics

115

141

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“…(26) and (27) in Eqs. (22,23), we see that each of F 1 and QF 2 contains an explicit factor of Q, and…”

Section: Proton Form Factorsmentioning

confidence: 99%

“…Such models have a long history [14][15][16], and many authors [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] have contributed to the necessary developments. Schlumpf's model is used because his power-law wave functions lead to a reasonably good description of the proton electromagnetic form factors, G E and G M , at all of the values of Q 2 where data were available as of 1992 [10][11][12].…”

Section: Relativistic Constituent Quark Model Of the Nucleonmentioning

confidence: 99%

Q2independence ofQF2/F1

Miller

Frank

2002

Phys. Rev. C

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“…This assumption is justified since in the weak binding [14] and the valence [15] approximations, the constituent quarks are moving with the same velocity inside the baryon. The heavy baryons spin wave functions, which are the LF generalization of the conventional constituent quark model spin-isospin functions, are explicitly given by [13] …”

mentioning

confidence: 99%

Pwave toSwave pion transitions of charmed baryons

Tawfiq

O’Donnell

1999

Phys. Rev. D

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The SU (2N f ) ⊗ O(3) constituent quark model symmetry of the light diquark system are used to analyze single pion transitions of Swave to S-wave and P-wave to S-wave heavy baryons. We show that the Heavy Quark Symmetry (HQS) coupling factors are given in terms of the three independent couplings g Σ Q Λ Q π , f Λ Q1 Σ Q π and f Λ * Q1 Σ Q π . Light-Front quark model spin wave functions are, then, employed to calculate these couplings and to predict decay rates of single pion transitions between charm baryon states.

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Relativistic model of nucleon and pion structure: Static properties and electromagnetic soft form factors

Cited by 94 publications

References 32 publications

Light-Cone Quantization: Foundations and Applications

Light-Cone Quantization: Foundations and Applications

Q2independence ofQF2/F1

Pwave toSwave pion transitions of charmed baryons

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