Abstract
In the present series of two papers we solve exactly Wilson's equations for a long-range effective hamiltonian. These equations arise when one seeks a fixed point of the Wilson's renormalization group transformations in the formulation of perturbation theory. The first paper has a general character. Wilson's renormalization transformation and its modifications are defined and the group property for them is established. Some topological aspects of the renormalization transformations are discussed. A space of “projection hamiltonians” is introduced and a theorem on the invariance of this space with respect to the renormalization transformations is proved.
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