Here the isospin summation is the same as above while the geometry in orbital space is given straightforwardly by the diagram of figure 5.17

As an example, for a system of nucleons and pions the pseudo Hamiltonian (1.50) in terms of the field operators could be

where H are the free field Hamiltonians of Chapter III and where we have introduced the artificial kinematical center of mass Hamiltonian (Chapter IV) in order to extract the intrinsic states. With a configuration space limited to four pions and one nucleon the energy matrix looks for example as shown on figure 6.1.

By now it is a generally accepted idea that hadrons are composite systems, the constituents of which have been called partons by Feynman. In this language our fields represent the partons. We will want to test for example a model based on the following partons :

We limit this list to the fields with quantum numbers corresponding to those of the first few lowest physical particles. For completeness we have included the A, although the spin 3/2 field is not treated in this work.

In the calculation the parton masses are parameters to be adjusted for fitting the physical masses. The parton configurational energies are used as a criterium to truncate the functional space. These energies are evaluated by taking N in the Os state as the reference energy, and roughly the energy scale of the harmonic oscillator basis to be hw = 2m 280 MeV, which yields a level spacing for the unperturbed Hamiltonian (which contains p only) of the order of magnitude of the pion mass. This way ▲ in the Os state is at an energy of about 2 effective quanta and the л, р, w at energies of 1, 4, 4 effective quanta respectively. These values are utilized below for the truncation.

π

2

n particles

occupied orbits) for the pion cloud up to 6 effective quanta with in state j1 etc... and total angular momentum J is given in Table VI.1 first column n denotes the number of effective quanta, i.e. the harmonic oscillator total principal quantum number N of the configuration plus the corresponding number of pion masses.