Renormalizability of effective scalar field theory

Journal Article · Tue Nov 15 04:00:00 EST 1994 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1994.1109· OSTI ID:57007

Ball, R D ^[1]; Thorne, R S ^[2]

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1. CERN, Geneva (Switzerland)
2. Rutherford Appleton Lab., Oxon (United Kingdom)

The authors present a comprehensive discussion of the consistency of the effective quantum field theory of a single Z{sub 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. They 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. They then demonstrate that the effective theory has a well-defined unitary and causal analytic S-matrix at all energy scales. They 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 {var_phi}{sup 4}-theory. 49 refs., 4 figs.

• OSTI ID: 57007
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 236; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
FIELD THEORIES
RENORMALIZATION
SCALAR FIELDS