Tadpole diagrams in constant electromagnetic fields

Abstract

Abstract:We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves differentiations of the latter class of diagrams with respect to the field strength tensor and contractions with derivatives of the one-particle irreducible part of the Heisenberg-Euler effective Lagrangian in constant fields. Specific examples include the two-loop addendum to the HeisenbergEuler effective action as well as a novel one-loop correction to the charged particle propagator in constant electromagnetic fields discovered recently. As an additional example, the approach devised in the present article is adopted to derive the tadpole contribution to the two-loop photon polarization tensor in constant fields for the first time.

Large N external-field quantum electrodynamics

“…The reason for this is that constant fields cannot transfer momentum to virtual charged particle loops. This and the demand of gauge invariance immediately implies that in momentum space the current j can be cast into the form [23]…”

“…(3.15) which need to be accounted for a reliable extraction of the strong field limit we make use of the results of ref. [23], which showed that any possible 1PR diagram in constant fields can be generated from lower loop order diagrams by repeated action of the operator (∂L 1PI /∂ F µν )∂/∂ Fµν . This operator adds an additional 1PI tadpole to a given lower loop diagram by trading a coupling to the external field F for a 1PI tadpole.…”

Reducible contributions to quantum electrodynamics in external fields

“…Recently, however, it was found that historical calculations had overlooked the possibility of one particle reducible (1PR) contributions to processes in constant background fields [30][31][32]. These contributions involve a tadpole, displayed in figure 1, attached somewhere in the corresponding Feynman diagram describing the process.…”

“…These have been used to study low energy photon amplitudes [24,25] and the structure of the quantum vacuum, see [26] for a recent review. Aside from this, the particle propagator can also be constructed exactly (non-perturbatively) in the presence of constant fields, plane waves, and other symmetric fields, allowing the calculation of a variety of electron-seeded and photon-seeded processes, see [26][27][28][29] for reviews.Recently, however, it was found that historical calculations had overlooked the possibility of one particle reducible (1PR) contributions to processes in constant background fields [30][31][32]. These contributions involve a tadpole, displayed in figure 1, attached somewhere in the corresponding Feynman diagram describing the process.…”

Electron-Positron Vacuum Instability in Strong Electric Fields. Relativistic Semiclassical Approach

“…The resulting dielectric and magnetic permittivities up to correction terms are Recently, Refs. [110][111][112] studied the role of the one-particle reducible (1PR) loop diagrams. In this scheme, Figure 8 shows the effective action up to four loops.…”