Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / In the first part of this thesis, I describe how to obtain a consistent high-temperature approximation for the effective potential which is used to investigate temperature induced phase transitions in quantum field theories. In order to obtain meaningful results, at high temperature, it is necessary to include multi-loop contributions even when the coupling constants of the theory are very small. I show that the dominant multi-loop contributions can be resummed in the formalism of the effective action for composite operators. I then use the resummed effective potential to study the phase transitions of the lambda theta 4 model, a theory describing self-interacting scalar fields, and of the Abelian Higgs Model, a gauge theory describing scalar electrodynamics. I conclude that, within this approximation, the phase transition in the lambda theta 4 model is second order or very weakly first order, whereas it is first order in the Abelian Higgs Model, with strength dependent on the magnitude of the couplings. The second part of the thesis is devoted to the investigation of systems of anyons, which are particles with fractional spin and anomalous (fractional) quantum statistics in two spatial dimensions. As a consequence of the difficulties introduced by the anomalous statistics, the complete energy spectrum is not known even for very simple anyonic systems. In order to gain information on these spectra, I use a perturbative approach in which the small parameter is the deviation of the statistics from the bosonic limit. In the case of anyons in an harmonic potential, I find a class of eigenstates whose energies can be evaluated perturbatively up to second order. The results of my analysis indicate a series of properties which might characterize general many-anyon systems, and could be used in attempts to understand the Fractional Quantum Hall Effect. / 2031-01-01

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