Coset space dimensional reduction

In this thesis we investigate two areas of application of the coset space dimensional reduction (CSDR) scheme. (i) In its earliest applications CSDR was used to obtain Yang-Mills-Higgs theories from pure Yang-Mills theories in higher dimensions. In certain models relationships between the parameters of the four dimensional theory were obtained. We consider the effect of one loop corrections to these models and find that the relationships do not survive beyond the tree level. (ii) More recently coset space dimensional reduction has found an application in Becchi-Rouet- Stora-Tyutin supersymmetry. An elegant framework for quantisation of gauge fields in which the gauge fixing and compensating ghosts arise automatically is over six-dimensional, superspace. Taking the coset space to be Sp(2)ΛT 2/Sp(2) the extended BRST transformations correspond to translations in the extra two coordinates. We apply this to two new cases. Firstly, we consider rank-R antisymmetric tensor gauge fields. After dimensional reduction we obtain two (R-1) fermionic ghosts, three (R-2) bosonic ghosts, down to (R+1) scalar ghosts. This is the correct ghost spectrum required to formally ensure unitarity of the theory. Secondly, we covariantly quantise spinor-vector gauge fields in infinite dimensional representations of OSp(4/2). After dimensional reduction we find the usual spectrum of Fadeev-Popov and Nielsen-Kallosh ghosts. Finally, we examine in general the inhomogeneous Grassmann rotation group Sp(2)ΛT 2 and its representations which underlie all the above applications. The states can be labelled by pseudomass and pseudospin while the physical state vectors correspond to wave packets over fermionic momentum.