Exact Results in Quantum Theory & Gravity

The Gross-Neveu model is a quantum field theory model of Dirac fermions in two dimensions with an interaction term of quartic type. The model is barely renormalizable and asymptotically free. I will present a new construction of this model in Euclidean signature in infinite volume. The construction is based entirely on the renormalization group flow equation. I express the Schwinger functions of the model in terms of the effective potential and construct the effective potential by solving the flow equation using the Banach fixed point theorem. In order to define a suitable space of functionals, in which the flow equation can be solved, I use the filtered non-commutative probability space. The construction does not involve cluster expansion or discretization of phase-space and is applicable to other barely renormalizable and asymptotically free purely fermionic theories such as the symplectic fermion model.