Formal Proof of an Exact Scale Invariance in the Nambu-Jona-Lasinio Model
Keiichi Akama
TL;DR
This paper proves that in the Nambu-Jona-Lasinio model, the renormalization group beta functions are zero at all orders due to the compositeness condition, fixing the effective couplings and ensuring scale invariance.
Contribution
It provides a rigorous proof of exact scale invariance in the Nambu-Jona-Lasinio model through the vanishing of beta functions at all orders.
Findings
Beta functions identically vanish in the model
Effective couplings are fixed and do not run with scale
Scale invariance is proven exactly
Abstract
We show that the renormalization group beta functions in the Nambu-Jona-Lasinio model identically vanish in all order due to the compositeness condition. Accordingly the effective coupling constants are entirely fixed and do not run with the renormalization scale.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematics and Applications