Renomalizabilty and triple/quadruple vertices

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SUMMARY

A Lagrangian is considered renormalizable if it includes only triple and quadruple vertices or a maximum of four powers of the fields. The renormalizability of a theory is contingent upon the dimensionality of the fields involved. For instance, a 4-fermion interaction, exemplified by the Fermi theory of weak interactions, is definitively non-renormalizable. Standard references for further reading include the textbook "An Introduction to Quantum Field Theory" by Peskin & Schröder.

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I read that a Lagrangian is renormalizable if it contains only triple and quadruple vertices, or at most four powers of the fields.
Where can I read more about the precise mathematical conditions?
 
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This depends on the dimensionality of the fields. A 4-fermion interaction (such as the one in the Fermi theory of weak interactions) is not renormalizable. This should be covered in any QFT textbook. Peskin & Schröder is pretty standard, but there are of course others too.
 
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