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Abstract
In chapter 1 I begin by discussing the basic ideas of quantum field theory (QFT). I provide a review of symmetries in physics and then move on to discuss the quark model. Chapter 2 is a review of lattice gauge theory with particular attention paid to lattice QCD. I begin by introducing lattice QCD, I then discuss some of the associated problems. I move on to discuss gauge fields on the lattice along with free lattice fermions. I then use this to define the lattice QCD action. I conclude this chapter by discussing how to reproduce the correct continuum physics. Chapter 3 discusses the basic numerical techniques employed in lattice simulations. I review methods for putting particles onto the lattice and conclude with a discussion of how to fit the resulting data. Chapter 4 reviews symmetries of the QCD Lagrangian, various forms of symmetry breaking in physics, the PCAC relation, the Goldberger-Treiman relation and the spontaneous breakdown of the axial symmetry. I move on to discuss sigma models and finally arrive at a basic chiral perturbation theory. I present research completed with my supervisor C. Allton and collaborators A.W. Thomas, D.B. Leinweber and R. Young in chapters 5 & 6. This work involves making lattice predictions for the hadronic mass spectrum using extrapolation techniques based on the predictions of chiral perturbation theory which have been developed by the Adelaide group.
