  We exactly solve Dyson-Schwinger equations for a massless quartic scalar
field theory. n-point functions are computed till n=4 and the exact propagator
computed from the two-point function. The spectrum is so obtained, being the
same of a harmonic oscillator. Callan-Symanzik equation for the two-point
function gives the beta function. This gives the result that this theory has
only trivial fixed points. In the low-energy limit the coupling goes to zero
making the theory trivial and, at high energies, it reaches infinity. No Landau
pole appears, rather this should be seen as a precursor, in a weak perturbation
expansion, of the coupling reaching the trivial fixed point at infinity. Using
a mapping theorem, recently proved, between massless quartic scalar field
theory and gauge theories, we derive some properties of the latter.
