Local Composite Operators And The Mass Gap Of The Gross-Neveu Model: Msc. Dissertation

The Local Composite Operator (LCO) formalism presents an alternative approach for renormalizing a Field Theory in which a dynamical symmetry breaking is induced. This last fact can be seen in the mass generation of the particles considered in the model studied (e.g, bosons or fermions) via an interaction with an auxiliar scalar field introduced appropriately into the respective generating functional. After doing this, the associated effective potential is studied so a vaccuum stabilization (related to the symmetry breaking) is obtained. All the phenomena mentioned above occur at zero temperature, which is an extremal and ideal regime. Thus, it is appropriate and quite important to analize the finite-temperature regime of the theory because some interesting features of the model happen when the system is heated up, as in the case of the well-known phase transitions due to symmetry restoration.