In this thesis, the effects of the Lorentz symmetry break down inthe gauge sector of QED in presence of a supercritical magneticfield are analyzed. We show that a photon anomalous magneticmoment is dynamically induced by a superstrong magnetic field. The possible interaction between the virtual electromagnetic radiation and the external magnetic field suggests that a background of virtual photons is a source of magnetization to the whole vacuum. The correspondingcontribution to the vacuum magnetization density is determined byconsidering the individual contribution of each vacuum polarizationeigenmode in the Euler-Heisenberg Lagrangian. Additional issuesconcerning the transverse pressures are analyzed. We alsodetermined the connection between the Hamilton and the standardLagrange formalism for a generic Quantum Field Theory. By means offunctional methods a systematic procedure is presented to identifythe full correlation functions, which depend on the momentumfields, as functionals of those usually appearing in the standardLagrange formalism.Within the same context, thePoincare generators are obtained and the connection between the formfactors and the boost operator is established. Considering thelatter, we note that what are usually called the pion square charge radii, defined from derivatives of the pion formfactor at zero squared momentum transfer, is completely blurred outby relativistic and interaction corrections, so that it is not clearat all how to interpret these quantities in terms of the pion chargedistribution.