On the Unsolvability of Bosonic Quantum Fields
Two general unsolvability arguments for interacting bosonic
quantum field theories are presented, based on Dyson-Schwinger
equations on the lattice and cardinality considerations.
The first argument is related to the fact that, on a lattice
of size N, the system of lattice Dyson-Schwinger equations
closes on a basis of "primitive correlators"
which is finite, but grows exponentially with N.
By properly defining the continuum limit, one finds
for N to infinity a countably-infinite basis of the
primitive correlators.