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Baryon Form
Factors in different forms of kinematics The standard way to explore the substructure of baryons and in general of any entity is to bombard it with projectiles that can probe its internal structure. In the case of baryons, e.g. nucleons, one can explore its electromagnetic structure, using for instance electrons, or one can also probe its "weak" structure, making use of neutrinos. Due to the small size of hadrons, let us say around 1 fm, a simple estimation of the velocities of the constituents inside them would tell us that those constitutents are moving quite fast and thus that a relativistic theory is in order. The problem then is how to build-in covariance into quantum mechanical quark models. There are in the literature many works dealing with this problem. A paper by Dirac from 1949 introduced three forms of introducing relativity, he called them the instant form, the front form and the point form. A way of understanding the difference between the different forms is to look into the kinematic subgroup of the Poincare group. In simple words, let us start with the Instant form, in instant form of kinematics the kinematic subgroup of the Poincare group is the group of translations and rotations at fixed time (the usual rotations and translations). So what we are saying is that when we introduce the interactions in the commutator relations of the Poincare algebra we do not have them in the "kinematic subgroup" (that is why it is kinematic). Therefore in instant form one does not need to know the interactions to know how to rotate or translate a system. In Point form the kinematic subgroup is the group containing rotations and boosts, while the translations (the momenta) are dynamic. That means it is easy to boost the system but it is not easy to translate it. In Front form the kinematic subgroup is the group that leaves invariant the light cone.
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Bibliography
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There are plenty of
resources: Original Dirac paper:(All Forms) Dirac paper Our Papers: (All Forms) We have compared the three forms of kinematic for baryon form factors: Check this two Review by Keister and Polyzou (All Forms) Published in Adv.Nucl.Phys.20:225-479,1991 Coester Papers: (Front Form) Papers by Chung, Coester et al Graz Group: (Point Form) The Iowa-Graz group, say Klink-Plessas et al., have explored in great detail the point form of kinematics together with the OBE model. Some relevant papers: Papers from the Graz group(related to FFactors) Roma Group: (Front Form) Simula, Cardarelli, Pace et al. have many works on light-front form. Some relevant papers: Papers from the Roma group(related to FFactors) Keister and Capstick (Front Form) They have explored in detail the Front form for electroexcitation of resonances Keister and Capstick A. Krassnigg Thesis: (All Forms, Point Form) Nice chapters on Point form and the description of the different forms. You can get it from his webpage |
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