On canonical quantum field theories

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Abstract
We consider time reversal invariant canonical quantum field theories in which π=φ. We show that if the theory has a mass gap, the vacuum is an analytic vector for the time zero field φ (f). With the additional assumptions of Poincaré covariance, cyclicity of the vacuum for the time zero fields, and a domain condition on the Hamiltonian, we show that the Schwinger functions of the theory determine a Euclidean covariant Markov field theory. We also consider the implications of a bound of the form ±φ (f)j⩽H+γ (f) for the behavior of the ground state at large field strength. We show that such a bound implies that the vacuum is an analytic vector for ‖φ (f) ‖j/2+1.