Abstract
We develop a collective field theory of a U(N) gauge field, which involves gauge-invariant operators only. We treat gauge-invariant path-ordered phase factors as collective fields on string space. The theory is formulated in such a way that in the N ..-->.. infinity limit the collective field theory exactly approaches the original U(N) gauge field theory. Even for finite N it is expected that it provides correct excitation energy and degeneracy for low-lying states. The final form of the collective field theory is a field theory of closed strings. Although our formalism is Lorentz noncovariant, it is manifestly gauge invariant. The present paper is devoted mainly to the formalism, although a few remarks for the actual calculations are given in the final section.
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