Emission of pairs of Minkowski photons through the lens of the Unruh effect

TL;DR

The paper investigates whether emission of photon pairs by accelerated charges, viewed from inertial observers, reveals the Unruh effect. It builds a detailed framework using scalar and electromagnetic field decompositions into Minkowski, Rindler, and Unruh modes, and computes first-order two-photon emission probabilities in both inertial and Rindler frames. For uniformly accelerated sources, the Minkowski two-photon emission is fully accounted for by Thomson-like scattering of Rindler photons in the Unruh thermal bath, with explicit rates ${P_M^S}/{T_ ext{tot}}=rac{rak{g}^2 a^3}{24\pi^4}$ and ${P_R^{S, ext{scatt}}}/{T_ ext{tot}}=rac{rak{g}^2 a^3}{48\null ext{pi}^4}$; absorption and emission channels vanish due to energy-momentum constraints. The energy spectra show distinct frame-dependent features: an inertial-frame peak in the emitted pair energy and a Rindler-frame distribution dominated by soft modes, governed by $ ho_R^{S, ext{scatt}}( ilde{ u})\, ext{and}\, ho_M^{S, ext{em}}(u)$ with $K_0$- and $K_{0}$-type Bessel functions. Overall, the work provides a concrete link between Unruh physics and laboratory radiation, highlighting that pair emission by accelerated charges offers a testable signature of the Unruh thermal bath, with clear predictions for both scalar and electromagnetic cases and distinct scaling with the proper acceleration $a$.

Abstract

We discuss the emission of pairs of photons by charges with generic worldlines in the Minkowski vacuum from the viewpoint of inertial observers and interpret them from the perspective of Rindler observers. We show that the emission of pairs of Minkowski photons corresponds, in general, to three distinct processes according to Rindler observers: scattering, and emission and absorption of pairs of Rindler photons. In the special case of uniformly accelerated charges, the radiation observed in the inertial frame can be fully described by the scattering channel in the Rindler frame. Therefore, the emission of pairs of Minkowski photons -- commonly referred to as Unruh radiation -- can be seen as further evidence supporting the Unruh effect.

Figures (4)

• Figure 1: Energy distribution for scattered Rindler particles of the Unruh thermal bath for different values of the source's proper acceleration.
• Figure 2: Energy distribution of the mean energy emitted in the inertial frame for different values of the source's proper acceleration.
• Figure 3: Energy distribution with fixed transverse momenta for the Rindler description of the electromagnetic case for different values of the electron's proper acceleration. Here, we have assumed $k_\perp=1$ eV and $k_\perp'=0.5$ eV. Note that $\rho_\perp^{E, \mathrm{scatt}}$ is symmetric under exchange of $k_\perp$ and $k'_\perp$ (see Eq. \ref{['Gscatt']}).
• Figure 4: Scattering rate of Rindler photons (with fixed transverse momenta) from the Unruh thermal bath by a uniformly accelerated electron as a function of the proper acceleration.