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Cosmological perturbation theory (CPT) is an important tool with which inhomogeneities that seed the observed structure of our universe can be studied. This thesis introduces the subject of CPT and discusses applications of this at both linear and second order. At linear order the evolution of the curvature perturbation around horizon crossing is examined. We study single field inflation models numerically, and compare the curvature perturbation at horizon crossing to that at the end of inflation. In addition, linear-order CPT is extended to the case of a multi-fluid system and an approximation for the velocities of the baryons and photons in the early universe as well as the strength of the electric field is found. We use second order CPT to study magnetogenesis. By using fully relativistic, non-linear CPT we show how magnetic fields are generated. This is done by presenting the first fully analytical calculation of the magnetic field at second order. Our results suggest that magnetic fields with strengths of the order of 10²⁷G and with scale dependence M ∝ k⁴ may be generated - findings which are largely in agreement with previous numerical results. We end by outlining possible extensions to this work, in particular related to the study of primordial magnetogenesis.

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Chiral perturbation theory allows us to probe the low energy properties of hadrons. In this thesis we have looked at the axial coupling constant (see chapter 4) and baryon number violation (see chapter 5).We calculated the axial coupling constant up to O(p^4) using the extended on mass shell renormalisation scheme in chiral perturbation theory. We also included the decuplet as an explicit degree of freedom. To fit the free parameters in our expression we used a combination of lattice and experimental data. We found that the fourth order corrections were quite large, and we struggled to produce an acceptable fit to the data. We also saw that the running of g_{A}^{pn} with M_\pi predicted by lattice QCD and ChPT at O(p^4) do not agree well. This is likely due to a combination of finite size effects impacting the low pion mass lattice data and the chiral perturbative series converging slowly. For our work on baryon number violation we looked at determining the values of two low-energy constants that appear in the baryon violating chiral Lagrangian. To do this, we matched our expression to lattice data. Previous determinations of the parameters had been done without calculating the effect of loops, ours was the first investigation to see what impact the loop diagrams would have. We found that our determinations of the parameters were in agreement with previous results, suggesting the effect of the loops is small. We also performed a chiral extrapolation, and found that our results were in agreement with previous results that did not account for loop corrections. This suggests that the impact of higher-order corrections is not significant for this baryon-number-violating process.

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. / The principal purpose of this thesis was to calculate certain mass differences of elementary particles in second order perturbation theory, within the framework of a gauge invariant theory of interactions. First we calculated the mass difference of the electron and the muon on the assumption that they have same bare mass and have different physical masses as a result of their interaction with a neutral vector meson field whose quantum is the phi meson. The previous attempts in this direction treated the muon and the electron unsymmetrically, which caused the ratio of the pion decay into (electron + electronic neutrino) to the pion decay into (muon + muonic neutrino) to have a value not permitted by the accuracy of the experimental results. Those calculations predicted also the value of the anomalous magnetic moment of the muon much higher than the experimental value. Our calculation, on the other hand, not only gives the mass difference of the muon and the electron in agreement with their experimental value but also does not run into any difficulty faced by the previous calculations. Secondly, generalizing the meaning of the electromagnetic interaction, we calculated the mass differences of the different members of every charge multiplet of the strongly interacting particles. Only with two adjustable parameters we have been able to predict the mass differences of the seven pairs of particles. Finally, we speculated on the origin of the masses of the phi and rho mesons. Using the coupling constants previously introduced, we calculated their masses in agreement with the experimental masses. We used the same cut-off parameter as was assumed for the electromagnetic mass splitting. / 2031-01-01

In this thesis we develop inverse scattering algorithms towards the ultimate goal of online diagnostic methods. The aim is to detect structural changes inside power transformers and other major power grid components, like generators, shunt reactors etc. Power grid components, such as large power transformers, are not readily available from the manufacturers as standard designs. They are generally optimized for specific functions at a specific position in the power grid. Their replacement is very costly and takes a long time. Online methods for the diagnostics of adverse changes of the mechanical structure and the integrity of the dielectric insulation in power transformers and other power grid components, are therefore essential for the continuous operation of a power grid. Efficient online diagnostic methods can provide a real-time monitoring of mechanical structures and dielectric insulation in the active parts of power grid components. Microwave scattering is a candidate that may detect these early adverse changes of the mechanical structure or the dielectric insulation. Upon early detection, proper actions to avoid failure or, if necessary, to prepare for the timely replacement of the damaged component can be taken. The existing diagnostic methods lack the ability to provide online reliable information about adverse changes inside the active parts. More details about the existing diagnostic methods, both online and offline, and their limitations can be found in the licentiate thesis preceding the present PhD thesis. We use microwave scattering together with the inverse scattering algorithms, developed in the present work, to reconstruct the shapes of adverse mechanical structure changes. We model the propagation environment as a waveguide, in which measurement data can be obtained only at two ends (ports). Since we want to detect the onset of some deformation, that only slightly alters the scattering situation (weak scattering), we have linearized the inverse problem with good results. We have calculated the scattering parameters of the waveguide in the first-order perturbation, where they have linear dependencies on the continuous deformation function. A linearized inverse problem with a weak scattering assumption typically results in an ill-conditioned linear equation system. This is handled using Tikhonov regularization, with the L-curve method for tuning regularization parameters. We show that localized one-dimensional and two-dimensional shape deformations, for rectangular and coaxial waveguide models, are efficiently reconstructed using the inverse scattering algorithms developed from the first principles, i.e. Maxwell’s theory of electromagnetism. An excellent agreement is obtained between the reconstructed and actual deformation shapes for a number of studied cases. These results show that it is possible to use the inverse algorithms, developed in the present thesis, as a theoretical basis for the design of a future diagnostic device. As a part of the future work, it remains to experimentally verify the results obtained so far, as well as to further study the theoretical limitations posed by linearization (first-order perturbation theory) and by the assumption of the continuity of the metallic waveguide boundaries and their deformations. / <p>QC 20160119</p>

By an orthodox application of the perturbation theory to the general case of a quantized field, it is shown that the divergence difficulty hitherto encountered arises from a faulty application of the expansion method. The difficulty disappears if the degeneracy of the unperturbed system is properly treated by the method of secular perturbation. Physically, it is shown that this amounts to a rigorous treatment of the radiation reaction.