Abstract
We investigate a fundamental nonlinear process of vacuum photon emission in the presence of strong electromagnetic fields going beyond the locally-constant field approximation (LCFA), i.e., providing the exact treatment of the spatiotemporal inhomogeneities of the external field. We examine a standing electromagnetic wave formed by high-intensity laser pulses and benchmark the approximate predictions against the results obtained by means of a precise approach evaluating both the tadpole (reducible) and vertex (irreducible) contributions. It is demonstrated that the previously used approximate methods may fail to properly describe the quantitative characteristics of each of the two terms. In the case of the tadpole contribution, the LCFA considerably underestimates the number of photons emitted for sufficiently high frequency of the external field. The vertex term predicts emission of a great number of soft photons whose spectrum is no longer isotropic in contrast to the LCFA results. A notable difference among the photon yields along different spatial directions, which is not captured by the LCFA, represents an important signature for experimental studies of the photon emission process. Since this feature takes place unless the Keldysh parameter is much larger than unity, it can also be used in indirect observation of the Schwinger mechanism.
Highlights
It is well known that Maxwell’s Lagrangian for electrodynamics leads to an inherently linear theory, and the corresponding superposition principle does not allow one solution of Maxwell’s equations to interact with another; i.e., a combination of two classical light waves does not give rise to any additional radiation
We investigate a fundamental nonlinear process of vacuum photon emission in the presence of strong electromagnetic fields going beyond the locally constant field approximation (LCFA), i.e., providing the exact treatment of the spatiotemporal inhomogeneities of the external field
The condition ðω=mÞ2 ≪ 1 justifying the LCFA was already discussed in the literature, the deviation between the LCFA predictions and the exact results was unknown as the latter data has been unavailable until now
Summary
It is well known that Maxwell’s Lagrangian for electrodynamics leads to an inherently linear theory, and the corresponding superposition principle does not allow one solution of Maxwell’s equations to interact with another; i.e., a combination of two classical light waves does not give rise to any additional radiation. The LCFA approach allows one to efficiently evaluate the tadpole (reducible) contribution [see Fig. 1(a)] to the spectra of signal photons taking into account the spatiotemporal dependence of complex field configurations. The corresponding expressions give essentially the leadingorder contributions to the photon number density, we will utilize here an alternative approach based on direct calculation of the mean value of the photon number operator Since the interaction Hamiltonian contains terms with only one photon creation/annihilation operator, it is clear that the first-order contribution to the number density (7) vanishes. The leading contribution is determined by the diagram with four external legs, which can be approximately calculated within the LCFA approach developed in Refs. Since the condition ðE0=EcÞ2 ≪ 1 seems completely realistic, there is no need to evaluate the higher-order terms
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