Exact Results in Quantum Theory

In standard quantum field theory, the Hilbert spaces of one-particle states correspond to irreducible unitary representations of the universal covering of the Poincare group, whereas quantum fields are classified by finite-dimensional representations of the universal covering of the Lorentz group. For a given field, these representations need to be connected vie Weinberg consistency conditions. I will investigate the possibility of using finite-dimensional faithful representations of the Poincare group to classify quantum fields. Is it possible to develop a consistent theory of the associated particles? If yes, will they differ from standard ones? This questions will be addressed.

I will also consider the inclusion of gravity, interpreted as a gauge theory of the Poincare group, to the field theories constructed in thisway. The new feature is that the translational gauge fields enter the covariant derivative of matter fields. Also, the so called Poincarecoordinates, that are normally hidden within the cotetrad (together with translational gauge fields) will now manifest themselves explicitly.