Ricerc@Sapienza

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.
The second argument in favor of the transcendency
of exact solutions, is that any conceivable exact analytic
calculation of the primitive correlators involves,
in the continuum limit, a linear system of coupled partial
differential equations with variable coefficients
on an infinite number of unknown functions,
namely the primitive correlators, evolving with respect to
an infinite number of independent variables.