This thesis is concerned with aspects of quantum effective field theories, effectiveactions, and their applications. New spin-flavor symmetries of the strong interactions,which arise in the limit of very large quark masses, can be incorporated into a heavyquark effective field theory (HQEFT). A general method for deriving the effectiveLagrangian of this theory to any order in 1/m_Q (where m_Q is the heavy quark mass)is developed; it is used to calculate terms up to order 1/m^3_Q. The renormalization ofterms in the Lagrangian to order 1/m^2_Q is performed. Such operators break these newsymmetries and consequently are important corrections to the leading-order predictions.HQEFT can be combined with chiral perturbation theory into a heavy mesonchiral perturbation theory (HMChPT) which describes the low-momentum interactionsof hadrons containing a heavy quark with pseudo-Goldstone bosons. HMChPTis used to investigate the semi-leptonic four-body decay of B and D mesons into finalstates with at least one Goldstone boson. Such processes may be utilized to testthe above heavy quark symmetries. The remainder of this dissertation deals with theevaluation of effective actions and their implications. A method to efficiently computethe one-loop effective action at zero and finite temperatures is elucidated. In a firstorder cosmological phase transition, the decay rate and the temperature at which itoccurs depends on the free energy of a critical bubble configuration. Since this freeenergy is related to the effective action but is usually approximated with an effectivepotential, the calculational method developed above is used to study the validity ofof this approximation. The corrections are found to be important for quantitativework.
