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The 1/N expansion in quantum field theory is formulated within an algebraicframework. For a scalar field taking values in the $N$ by $N$ hermitianmatrices, we rigorously construct the gauge invariant interacting quantum fieldoperators in the sense of power series in 1/N and the `t Hooft couplingparameter as members of an abstract *-algebra. The key advantages of ouralgebraic formulation over the usual formulation of the 1/N expansion in termsof Green's functions are (i) that it is completely local so that infra-reddivergencies in massless theories are avoided on the algebraic level and (ii)that it admits a generalization to quantum field theories on general Lorentziancurved spacetimes. We expect that our constructions are also applicable inmodels possessing local gauge invariance such as Yang-Mills theories.  The 1/N expansion of the renormalization group flow is constructed on thealgebraic level via a family of *-isomorphisms between the algebras ofinteracting field observables corresponding to different scales. We alsoconsider $k$-parameter deformations of the interacting field algebras thatarise from reducing the symmetry group of the model to a diagonal subgroup with$k$ factors. These parameters smoothly interpolate between situations ofdifferent symmetry.Comment: 52 pages, Latex, 4 figures, includes self-contained review of the  operator algebraic approach to perturbatively defined quantum field theory in  Minkowski spacetime, updated versio

ALGEBRAIC APPROACH TO THE 1/N EXPANSION IN QUANTUM FIELD THEORY