Aspectos dimensionais da massa do fóton na eletrodinâmica quântica

Abstract

The gauge invariance of Quantum Electrodynamics establishes a non massive character for the photon field. Nevertheless, corrections at one loop level for the self-energy of the photon can induce mass generation in some space-time dimensions. The aim of this work is to study this aspect of quantum electrodynamics calculating the vacuum polarization tensor and performing the renormalization of the propagator through the correction at one loop level for the self-energy of the photon in space-time dimensions 2, 3, 4 and 5. The calculations of perturbative amplitudes relevant to this work presenting divergent character will be made a strategy alternative to the traditional methods of the literature. This method, proposed and developed by Professor O. A. Battistel has been successfully used in many contexts of the perturbative calculation in Quantum Field Theory presenting significant advantages relative to the usual ones because it does not introduce changes in the forms provided by the Feynman rules. It also allows automatically to eliminate the well known intrinsic ambiguities of the perturbative amplitudes , when the degree of divergence which are involved is higher than the logarithmic, terms which are potentially symmetry violators. With this, it allows clean and transparent conclusions in investigations where the use of regularization contaminates the results and forbiden the establishment of physical consequences of theories through the perturbative solutions. The basic physical processes of the theory are treated making up the calculations of different amplitudes with the most general possible choices for the internal lines momenta. The inherent arbitrarities of perturbative calculations are preserved during the intermedially operations since divergent integrals are not realy calculated. For the manipulations performed is only assumed the presence of an implicitly regulating function. Through relationship between Green’s functions, symmetry relations and determinations of general theorems, we can determine relations among different integrals with the same degree of divergence necessary and sufficient for the desired consistency in the perturbation calculation. As a consequence we see the unevitable change, in an unambiguous way, of the Lorentz structure of photonic propagator, through the induction of a Chern-Simons term in the calculation of the vacuum polarization tensor in three dimensions, which has as a consequence of dynamic generation of mass for the photon.