Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




John D Walecka


The linear sigma model and its extension, Quantum Hadro-dynamics 3 (QHD-III) are discussed. QHD-III is a gauge-invariant model of the strong interaction based on the linear sigma model, which is made locally invariant under SU(2)L x SU(2)R. Parity conservation is imposed. The gauge bosons rho and a1 are made massive via a Higgs mechanism as in the standard model. The low-energy symmetries of QCD, the ability to evaluate corrections coming from meson loops and the derivation of unambiguous conserved currents is used to motivate QHD-III. A renormalized pipi scattering amplitude to 1-loop using Feynman diagrams in the linear sigma-model is derived. The renormalized corrections due to vector boson exchange are also calculated in QHD-III and explicitly shown to be negligible when their masses become large. The pion decay constant to 1-loop is also calculated and discussed. The gauge invariance of the theory is analyzed and exploited to identify the physical pion and to considerably simplify the QHD-III lagrangian. The 1-loop effective action of the linear sigma model is derived and its predictions are shown to be identical to the amplitudes calculated using Feynman diagrams. The 1-loop effective action of QHD-III is discussed and shown to provide an explicit proof of the decoupling theorem.



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