Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-10-07
Annals Phys. 236 (1994) 117-204
Physics
High Energy Physics
High Energy Physics - Theory
80 pages, TeX, OUTP-93-23P, CERN-TH.7067/93. Many minor revisions, and several new paragraphs
Scientific paper
10.1006/aphy.1994.1109
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.
Ball Richard D.
Thorne Robert S.
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