The phase transition temperature for the Bose-Einstein condensation (BEC) of weakly-interacting Bose gases in three dimensions is known to be related to certain non-universal properties of the phase transition of three-dimensional O(2) symmetric φ 4 theory. These properties have been measured previously in Monte Carlo lattice simulations. They have also been approximated analytically, with moderate success, by large N approximations to O(N ) symmetric φ 4 theory. To begin investigating the region of validity of the large N approximation in this application, I have applied the same Monte Carlo technique developed for the O(2) model (Ref.[5]) to O(1) and O(4) theories. My results indicate that there might exist some theoretically unanticipated systematic errors in the extrapolation of the continuum value from lattice Monte Carlo results. The final results show that the difference between simulations and NLO large N calculations does not improve significantly from N = 2 to N = 4. This suggests one would need to simulate yet larger N 's to see true large N scaling of the difference. Quite unexpectedly (and presumably accidentally), my Monte Carlo result for N = 1 seems to give the best agreement with the large N approximation among the three cases.
A method for constructing a complete set of relativistic three-quark states in light front dynamics is implemented for the nucleon, N * (1520) and N * (1535). This approach facilitates constructing states containing virtual antiquarks and a physical interpretation is provided in terms of transition amplitudes from quark to quark-gluon or quark-Goldstone boson Fock states of chiral dynamics generated by flux tube breaking expected in QCD at intermediate distances.
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