Ambiguities and symmetry relations in the perturbative solution of Quantum Electrodynamics

Divergent Integrals Treatment in Quantum Field Theory

“…Now we consider the QED Lagrangian. In the case of QED [11], we chose the diagram in the Figure 2 because it has a cubic divergence. Another reason for choosing this diagram is that it is related to the following theorem and the following symmetry relation.…”

“…We need to check only relations (16) and (18). The left side of (18) regularized results in (11). On the right side of (18), we have…”

“…The first fails to preserve symmetries, the second respects symmetries but presents difficulties with the spacetime dimensionality and a third that, if we take some care, respects symmetries and can be used without restriction in any space-time dimension. The methods are: the regularization of Pauli Villars [8], a pioneer of regularization methods; Dimensional Regularization (DR) that preserves the symmetries of QED; and the Implicit Regularization Method (IR) [9][10][11][12]. In the latter we say that the integral is regularized for the purposes of algebraic manipulations, but we do not need to use any regularization method explicitly.…”

Mass scales and their relations in symmetric quantum field theory

“…In a general way this fact allows to establish algebraic relations among the subtraction constants of the divergent Green functions of a theory and, therefore, it is a useful tool in the renormalization procedure. Nevertheless Ward Identities can be violated by some used regularization scheme [7] like gauge symmetry in the Quantum Electrodynamics. For the linear sigma model chiral symmetry it is really regularization independent.…”