Field theory renormalization group: the Tomonaga-Luttinger model revisited

We apply field theoretical renormalization group (RG) methods to describe the Tomonaga-Luttinger model as an important test ground to deal with spin-charge separation effects in higher spatial dimensions. We calculate the RG equations for the renormalized forward couplings g(2R) and g(4R) up to two-loop order and demonstrate that they do not flow in the vicinities of the Fermi points (FPs). We solve the Callan-Symanzik equation for G((a)R) in the vicinities of the FPs. We calculate the related spectral function and the momentum distribution function at p = k(F), p(0) = omega. We compute the renormalized one-particle irreducible function Gamma((2))((+)R) (p, p(0) = 0; Lambda) and show that it carries important spin-charge separation effects in agreement with well-known results. Finally, we discuss the implementation of the RG scheme taking into account the important simplifications produced by the Ward identities.