Citation
Hill, Roger Calvert (1969) Relativistic quark models and the current algebra. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MHB7G746. https://resolver.caltech.edu/CaltechTHESIS:03182016143936721
Abstract
In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axialvector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.
We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any twoquark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).
In the freequark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m^{3}. However, it may be possible to solve the factorized SU(2) problem with this model.
The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4momentum, which seem unphysical.
Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Physics  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Physics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  4 June 1968  
Funders: 
 
Record Number:  CaltechTHESIS:03182016143936721  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:03182016143936721  
DOI:  10.7907/MHB7G746  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9625  
Collection:  CaltechTHESIS  
Deposited By:  Leslie Granillo  
Deposited On:  21 Mar 2016 16:53  
Last Modified:  21 Dec 2019 01:41 
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