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We demonstrate that in asymptotically free gauge theories the wave-function renormalization constants for spin-1/2 fields do not vanish. (The scalar fields, if incorporated, also have this property.) However, there exists a subclass of such theories where the Z's for the gauge fields themselves tend to zero in the limit of infinite cutoff. These features are shown to be gauge-independent. This suggests the potentiality of constructing asymptotically free strong-interaction theories in which the only elementary fields are "quarks" and all other hadrons are bound states.
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Cheng et al. (1974) studied this question.
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