Bremsstrahlung 2026-10-06
Bremsstrahlung is electromagnetic radiation emitted when a charged particle accelerates during interaction with another charged particle or field. The microscopic process creates a photon, while its inverse absorbs one. Thus it contributes to a photon-number collision source in the photon number current, unlike ordinary Compton scattering. Thermal bremsstrahlung averages this emission over a thermal distribution of charged particles.
Double Compton scattering 2026-10-06
Double Compton scattering is , together with its inverse. The forward reaction has one incoming and two outgoing photons, so it changes their number and can source the divergence of the photon number current. Ordinary Compton scattering has one incoming and one outgoing photon and conserves photon number. Forward and inverse rates can balance without either reaction individually conserving it.
In the local orthonormal tetrad, the components of the photon number current are
They are respectively the photon number density and the photon number flux. Thus is the photon number four-current, not an energy current or an electric charge current. Photons carry no electric charge. For the isotropic background,
Integrating the covariant Boltzmann equation over the invariant mass-shell measure, with vanishing momentum-boundary flux, gives
where is the collision operator in the covariant streaming equation. Therefore
Collisionless photon propagation satisfies this condition, as do Thomson scattering and ordinary Compton scattering when all participating photons are counted: each collision has one incoming and one outgoing photon. Photon emission, photon absorption, bremsstrahlung, double Compton scattering and electron-positron annihilation in cosmology or its inverse generally give a nonzero number source. A cancellation of net creation and destruction can nevertheless make the integrated source vanish even when individual number-changing reactions occur. Cosmological redshift itself changes photon energy, not photon number; in an expanding homogeneous universe a conserved photon number current gives .
Photon emission 2026-10-06
Photon emission creates a photon, for example in bremsstrahlung or the decay of an excited material state. It produces a positive photon-number collision source when not balanced by inverse processes. The photon number current is conserved only if its integrated creation and destruction rates cancel.