New approach to effective field theories

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Abstract
A systematic discussion of effective field theories, describing a given subset of fields of a quantum field theory, is presented within the context of functional integration. Effective field theories are divided into two classes, natural and unnatural, according to certain independence properties of the counterterms of the theory, defined by minimal subtraction. Natural effective field theories allow independent renormalizations for two distinct mass scales of the theory. A set of constraints, which place restrictions on masses and external momenta, allow the effective field theory to be approximated by a local Lagrangian of dimension four. Predictions of the complete theory are compared with those of the local, effective theory in a domain where both are supposed to be valid. The separate renormalization-group improvement with respect to the two independent mass scales of a natural effective field theory is described. Special problems raised by the presence of massless Goldstone bosons are discussed. The general issues are illustrated by examples from scalar field theories in order to present the discussion simply.