Exact Results in Quantum Theory

Standard QFT relies heavily on the Poincare symmetry. This is taken to the extreme in Wigner's definition of particles as unitary irreducible representations of the Poincare group, which is now adopted in many handbooks of QFT, such as the one by Weinberg. Also, more mathematically oriented approaches, e.g. based on Wightman axiomatics, usually use the Poincare symmetry. This state of affairs is unfortunate when one tries to include gravity, in the presence of which the space-time symmetry group may be different from the Poincare, or may not exist at all. Also, when gravity itself is to be quantized in a background independent way, the space-time symmetries cannot be used.It is natural to ask whether it is unavoidable or just convenient to use the Poincare symmetry in QFT. I will present the consequently canonical and Poincare-free quantization of spinor electrodynamics. Some difficulties will appear due to the presence of constraints and spinorial matter. The techniques that will be used to deal with these problems are certainly not a novelty, but they are presented surprisingly rarely in standard treatments of QFT.