Browsing by Author "Stoddart, A J"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Open Access
    Perturbative quantum chromodynamics in a cavity
    (1987) Stoddart, A J; Viollier, R D
    BRS invariant Quantum Chromodynamics is quantized in a static spherical cavity, subject to the boundary conditions of the MIT group. Using the Gell-Mann and Low theorem and a modified version of Goldstones theorem we formulate perturbation theory. In 4th order perturbation theory we calculate the Feynman diagrams corresponding to configuration mixing-and two gluon annihilation. The results are inserted into the MIT bag model and compared with hadron spectra.
  • Thumbnail Image
    Item
    Open Access
    Renormalization of cavity field theories
    (1990) Stoddart, A J; Viollier, Raoul D
    A major obstacle to calculating Feynman diagrams in field theories, confined to a cavity, has always been the divergent loop diagrams. So far, only the quantum chromodynamic and electrodynamic self-energies of a ls1/2 quark, confined to a static spherical cavity, have been accurately calculated. These quantities are of immediate interest in the M.I.T. bag model. The existing methods to calculate loop diagrams are based on the multiple reflection scheme, in which the zero reflection term is separated out analytically, and evaluated separately. Thus far, there are some indications that this method is unsuitable for the quadratically divergent one loop vacuum polarization. In this thesis we firstly develop a set of Fourier transforms, appropriate to a discussion of renormalization in a cavity. Using these, we renormalize the cavity propagators to one loop for scalar, Dirac, and gauge fields. We then introduce a new computational method to subtract out the divergences, based on dimensional regularization. Using this method, we present results for various loop diagrams. The scalar φ⁴ theory is used as a pedagogical example. We then present the quark self-energy for several low lying cavity modes. Finally we tackle the long standing and hitherto unresolved question of the vacuum polarization. For this we give a detailed discussion of surface divergences, and present results for scalar quantum electrodynamics. We make a suggestion for the implementation of the running coupling constant in the cavity.