The energy momentum spectrum and vacuum expectation values in quantum field theory, II (original) (raw)

We prove that the 0>(φ) 2 quantum field theory satisfies the spectral condition. The space time translation a = (x, t) is implemented by the unitary group U(a) = exp(ίtH -ixP), and the joint spectrum of the energy operator H and the momentum operator P is contained in the forward cone. We also obtain bounds on certain vacuum expectation values of products of field operators. Our proofs involve an analysis of the limit F->-oo for approximate theories in a periodic box of volume V. Assuming the existence of a uniform mass gap, we are able to establish all the Wightman axioms with the exception of the Lorentz invariance of the vacuum.