A gauge invariant flow equation

Given a Quantum Field Theory, with a particular content of fields and a symmetry associated with them, if one wants to study the evolution of the couplings via a Wilsonian renormalisation group, there is still a freedom on the construction of a flow equation, allowed by scheme independence. In the present thesis, making use of this choice, we first build up a generalisation of the Polchinski flow equation for the massless scalar field, and, applying it to the calculation of the beta function at one loop for the characteristic self-interaction, we test its universality beyond the already known cutoff independence. Doing so we also develop a method to perform the calculation with this generalised flow equation for more complex cases. In the second part of the thesis, the method is extended to SU(N) Yang-Mills gauge theory, regulated by incorporating it in a spontaneously broken SU(N|N) supergauge group. Making use of the freedom allowed by scheme independence, we develop a flow equation for a SU(N|N) gauge theory, which preserves the invariance step by step throughout the flow and demonstrate the technique with a compact calculation of the one-loop beta function for the SU(N) Yang-Mills physical sector of SU(N|N), achieving a manifestly universal result, and without gauge fixing, for the first time at finite N.Comment: PhD thesis, Latex, 175 page

Non-relativistic bound states: the long way back from the Bethe-Salpeter to the Schroedinger equation

I review, in a personal perspective, the history of the theory of non-relativistic bound states in QED and QCD from the Bethe-Salpeter equation to the construction of effective field theories.Comment: Contribution to "Fundamental Interactions - A Memorial Volume for Wolfgang Kummer", D. Grumiller, A. Rebhan, D.V. Vassilevich (eds.); 17 pages, 6 figures; references adde

The Intermediate Band Solar Cell: Progress Toward the Realization of an Attractive Concept

The intermediate band (IB) solar cell has been proposed to increase the current of solar cells while at the same time preserving the output voltage in order to produce an efficiency that ideally is above the limit established by Shockley and Queisser in 1961. The concept is described and the present realizations and acquired understanding are explained. Quantum dots are used to make the cells but the efficiencies that have been achieved so far are not yet satisfactory. Possible ways to overcome the issues involved are depicted. Alternatively, and against early predictions, IB alloys have been prepared and cells that undoubtedly display the IB behavior have been fabricated, although their efficiency is still low. Full development of this concept is not trivial but it is expected that once the development of IB solar cells is fully mastered, IB solar cells should be able to operate in tandem in concentrators with very high efficiencies or as thin cells at low cost with efficiencies above the present ones