Connection between the spectrum condition and the Lorentz invariance of P(phi)_2

by R. F. Streater, Commun. in Mathematical Phys., 26, 109-120, 1972.

ABSTRACT

We prove that, for the P(phi) quantum field theory in two space-time dimensions, the Wightman functions are Lorentz invariant if the energy-momentum spectrum lies in the forward light-cone. The ingredients of the proof are the following facts, established by Glimm and Jaffe: the field satisfies local commutativity, and also the estimates

phi_V(f,t)< const ||f||_1(H_V+1)

pi_V(g,t)< ||g||_2(H_V+1)

where V is a space cut-off, uniformly in V, and pi is the time-derivative of the field (that is, pi is the conjugate momentum field).

Note. In the event, the proof of Lorentz invariance of the theory was proved by a different method. But Osipov used this method to give the first proof of the Lorentz covariance of Y_2.