Derivative corrections to the Heisenberg-Euler effective action

We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak- and strong-field expansions can be worked out. One immediate application is the leading derivative correction to the renowned Schwinger-formula describing the decay of the quantum vacuum via electron-positron pair production in slowly-varying electric fields.

Scalar quantum electrodynamics via Duffin–Kemmer–Petiau gauge theory in the Heisenberg picture: Vacuum polarization

Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced current for the case of a charged scalar field in the presence of an external electromagnetic field. Charge renormalization is brought into discussion for the interpretation of the results for the vacuum polarization.

Consistency and universality in odd and even dimensional space–time QFT perturbative calculations

The questions related to the consistent interpretation of QFT perturbative amplitudes are considered in light of a novel procedure, alternative to the traditional ones based on regularization prescriptions. A detailed discussion about the aspects associated to the space–time dimension is performed. For this purpose, it is considered a simple model having a fermionic vector current, coupled to a vector field, as well as a fermionic scalar current, coupled to a scalar field, both of them composed by different species of massive fermions. The referred currents are related in a precise way, which is reflected in the Ward identities for the perturbative physical amplitudes. The double vector two-point fermionic function, related to the vacuum polarization tensor of QED, as well as the amplitudes related to such quantity through relations among Green functions are explicit evaluated in space–time dimensions d = 2, 3, 4, 5 and 6. In the adopted procedure the perturbative amplitudes are not modified in intermediary steps of the calculations, as occurs in regularization procedures. Divergent Feynman integrals are not really solved. They appear only in standard objects, conveniently defined, where no physical parameter is present. Only very general properties for such quantities are assumed. For the finite parts, a set of functions is introduced which allows universal forms for the results. We show that scale independent, ambiguity free amplitudes are automatically obtained in a regularization independent way. As a consequence, interesting and, in certain way, surprising aspects are revealed in a clear and transparent way when the Ward identities and low-energy limits are verified for the simple amplitudes considered in the presently reported investigation. The obtained results suggest that the procedure can be considered as an advantageous tool to handle with the problem of divergences in perturbative solutions of QFT's, relative to the traditional regularization techniques, since the obtained results are so consistent as desirable and there are no limitations of applicability. In particular, the method can be applied in odd and even space–time dimensions having extra dimensions, which is not possible within the context of traditional regularization.

AMBIGUITIES AND SYMMETRY RELATIONS IN FIVE-DIMENSIONAL PERTURBATIVE CALCULATIONS: THE EXPLICIT EVALUATION OF THE QED5 VACUUM POLARIZATION TENSOR

An explicit evaluation of the D = 4+1 quantum electrodynamics (QED) vacuum polarization tensor is presented. The calculations are made preserving all the intrinsic arbitrariness involved in such type of problem. The internal momenta are assumed arbitrary in order to preserve the possibility of dependence on such kind of choice, due to the superficial degree of divergence involved. An arbitrary scale is introduced in the separation of terms having different degrees of divergences in order to preserve the possibility of scale ambiguities. In the performed steps the effects of regularizations are avoided by using an adequate strategy to handle the problem of divergences in Quantum Field Theory perturbative calculations. Given this attitude it is possible to get clean and sound conclusions about the consistency requirements involved in perturbative calculations D = 4+1 space–time dimension. At the final a symmetry preserving and ambiguities free result is obtained allowing the renormalization of the photon propagator at the one-loop level. The simplicity added to the general character of the adopted procedure allows us to believe that the referred strategy can be used without restrictions of applicability in perturbative calculations made in theories formulated in a space–time having extra dimensions relative to the physical one (D = 3+1) producing consistent results, in odd and even dimensions, in spite of the nonrenormalizable character.

A NUMERICAL EVALUATION OF VACUUM POLARIZATION TENSOR IN CONSTANT EXTERNAL MAGNETIC FIELDS

Hattori–Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exceeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an O(10-2) level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.