PERTURBATIVE RENORMALIZATION GROUP FUNCTION IN THE MOST
GENERAL FOUR-FERMION INTERATIONS MODEL IN (1+1)D
Van Sérgio Alves¹, Carlos André Bahia Leandro¹, Leonardo O. Nascimento² and Francisco Peña³
1
Faculdade de Física, Universidade Federal do Pará, Belém, Brasil,[email protected]
Faculdade de Física, Universidade Federal do Pará, Belém, Brasil,[email protected]
² IFPA, [email protected]
³ Departamento de Ciências Físicas, Facultad de Ingeniería, Ciencias y Administracíon,
Universidad de La Fronteira, Temuco, Chile, [email protected]
1
The importance of studying models in quantum field theory in two space-time dimensions, lies not
only in the academic aspect but also the fact that in low dimensions they are more easily
investigated and in some cases they can be solved exactly. This means that field theories in low
dimensions are a good laboratory for the study of general properties and also in discovering of
the new aspects that could be relevant in higher dimensions. The purpose of this work is to study
the perturbative behavior of the beta function at 1-loop order and analyze the structure of fixed
points in the most general four-fermion interactions obeying an $U(N)$ symmetry, given by the
following
Lagrangean:
${\cal
L}=\bar\psi_{a}(i\gamma^{\mu}\partial_{\mu}-m)\psi_{a}\frac{1}{2}g_{1}(\bar\psi_{a}\psi_{a})^{2}-\frac{1}{2}g_{2}(\bar\psi_{a}\gamma^{5}\psi_{a})^{2}\frac{1}{2}g_{3}(\bar\psi_{a}\gamma^{\mu}\psi_{a})^{2}$, where a sum on repeated flavors indices
is explicit, and the fermions transform under the fundamental representation of $U(N)$ group.
This model has all special cases known in literature, such as the Gross-Neveu model, the Thirring
model, the chiral Gross-Neveu model and the non-abelian Thirring model. We clarify the tensorial
structure of the interaction vertices and calculate the functions of the renormalization group. We
use the Zimmermann's procedure for reducing the coupling constants.
Palavras-chave: Four férmions model, Renormalization group functions, Reduction of coupling
constants.