Abstract
An approximate RG equation is derived and studied in scalar quantum field theories in d dimensions. The approximation allows for an infinite number of different couplings in the potential, but excludes interactions containing derivatives. The resulting non-linear partial differential equation can be studied by simple means. Both the gaussian and the non-gaussian fixed points are discribed qualitatively correctly by the equation. The RG flows n d = 4 and the problem of defining an “effective” field theory are discussed in detail.
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