A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2015. / Recently there has been signi cant interest in new types of metals called non-Fermi
liquids, which cannot be described by Landau Fermi liquid theory. Landau Fermi
liquid theory is a theoretical model used to describe low energy interacting fermions or
quasiparticles. There is a growing interest in constructing an e ective eld theory for
these types of metals. One of the paradigms to understand these metals is by the use
of Wilsonian renormalization group (RG) to study a theoretical toy model consisting
of fermions coupled to a gapless order parameter eld. Here we will study fermions
coupled to gapless bosons (order parameter) below the upper critical dimension (d =
3). We will treat both fermions and bosons on equal footing and construct an e ective
eld theory which only integrates out high momentum modes. Then we compute
the one-loop RG
ows for the Yukawa coupling and four-Fermi interaction. We will
discuss log2 and log3 subleties associated with the one loop RG
ows for the four-Fermi
interaction and how they can be circumvented.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/18572 |
| Date | 02 1900 |
| Creators | Rabambi, Teflon Phumudzo |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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