Summary
We give a simple combinatorial proof of the renormalization group equation in the minimal subtraction scheme. Being mathematically rigorous, the proof avoids both the notorious complexity of techniques using parametric representations of Feynman diagram and heuristic arguments of usual «proofs» calling up bare fields living in the space-time of complex dimension. It also copes easily with the general case of Green's functions of an arbitrary number of composite fields.
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Chetyrkin, K.G. A simple proof of renomalization group equation in the minimal subtraction scheme. Nuov Cim A 103, 1653–1667 (1990). https://doi.org/10.1007/BF02887290
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DOI: https://doi.org/10.1007/BF02887290