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On the ultraviolet problem for the 2D weakly interacting fermi gas
No full textWe prove that the effective potential of the two-dimensional interacting continuous Fermi gas with infrared cutoff is an analytic function of the coupling strength near the origin. This is the starting point to study the infrared problem of the model without putting any ultraviolet cutoff, as usually done in the literature
Rigorous analysis of the Tomonaga model by means of Ward identities and the renormalization group
No full textRenormalization group
No full textThe notion of renormalization group is not well
defined. It arises in theories in which a prominent role is
played by scale invariance or covariance properties,
of various quantities, with respect to a noninvertible transformation
of coordinates. The noninvertibility is an essential feature; it is
supposed to allow one to reduce effectively the difficulty of the problem.
The Book illustrates important examples of the method
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