Noncovariance of field theories quantized on the light cone which are not scale invariant

It is shown from spectral representations involving the energy-momentum tensor that in general a field theory quantized on the light cone (as opposed to the case in which an equal-time-quantized theory is merely rewritten in terms of light-cone coordinates) does not possess a Lorentz-invariant vacuum state. The sole exception to this result occurs in cases for which one has scale invariance.