On the Quantisation of Spin Gauge Theory

Abstract

In this work the renormalisability of Spin Gauge Theory (SGT) is examined in first loop order. This theory has been developed in 1995 by Dehnen and Hitzer in order to attempt quantisation and thus unification of gravity with the other fundamental forces. It has been shown that Einstein's theory of General Relativity is not renormalisable. Thus, to obtain a quantum theory of gravity, one has to modify either the foundations of quantum field theory or (as is done in this work) of General Relativity. SGT is such an alternative (microscopic) theory of gravitation from which General Relativity (up to now only in linearised form) emerges in its macroscopic limit. Gravitons are represented as excitations of a tensor valued Higgs field that couple to the kinetic term of the fermions. At the beginning of this work SGT is introduced as a classical field theory. Then the quantisation is performed by means of the standard path integral method. Already at this point the theory shows some peculiarities linked to the derivative coupling between fermions and gravitons: the theory cannot be quantised at the symmetrical point, but symmetry breaking has to be performed before quantising the excitations of the Higgs field from the physical ground state. Thus the theory contains 1-point functions that vanish only after renormalisation.After performing dimensional regularisation it is investigated whether the theory is renormalisable. It is shown that the free graviton field (including self-interactions) is not renormalisable in its present form, but that minor modifications of the Lagrangian may lead to a renormalisable theory. The interaction term of gravitons and fermions on the other hand leads (due to the derivative coupling) to divergencies that make the theory clearly nonrenormalisable.