  We present a comprehensive discussion of the consistency of the effective
quantum field theory of a single $Z_2$ symmetric scalar field. The theory is
constructed from a bare Euclidean action which at a scale much greater than the
particle's mass is constrained only by the most basic requirements; stability,
finiteness, analyticity, naturalness, and global symmetry. We prove to all
orders in perturbation theory the boundedness, convergence, and universality of
the theory at low energy scales, and thus that the theory is perturbatively
renormalizable in the sense that to a certain precision over a range of such
scales it depends only on a finite number of parameters. We then demonstrate
that the effective theory has a well defined unitary and causal analytic
S--matrix at all energy scales. We also show that redundant terms in the
Lagrangian may be systematically eliminated by field redefinitions without
changing the S--matrix, and discuss the extent to which effective field theory
and analytic S--matrix theory are actually equivalent. All this is achieved by
a systematic exploitation of Wilson's exact renormalization group flow
equation, as used by Polchinski in his original proof of the renormalizability
of conventional $\varphi^4$-theory.
