Kinoshita-Lee-Nauenberg theorem
The Kinoshita-Lee-Nauenberg theorem , or KLN theorem for short , is a proposition from quantum field theory . It says that complete scattering amplitudes do not diverge in the infrared limit , since different divergent components of the scattering amplitude cancel each other out exactly. These divergent components are the real, "soft" corrections from the absorption or radiation of low-energy and collinear photons or gluons and loops of virtual particles with low momentum. In technical jargon, the expression that the amplitudes are "IR-safe" is used.
The Kinoshita-Lee-Nauenberg theorem was independently proven in 1962 by Tōichirō Kinoshita and in 1963 by Tsung-Dao Lee and Michael Nauenberg . For the ultraviolet range, that is, for loops of virtual particles with high momentum, there is no theorem equivalent to the KLN theorem; these must be renormalized .
A related sentence to the Kinoshita-Lee-Nauenberg theorem is the Bloch-Nordsieck theorem , which in the special case of quantum electrodynamics ensures the mutual cancellation of the IR-divergent components from virtual loops and the emission of photons.
Individual evidence
- ↑ Toichiro Kinoshita: Mass Singularities of Feynman Amplitudes . In: Journal of Mathematical Physics . tape 3 , no. 4 , 1962, pp. 650 - 677 , doi : 10.1063 / 1.1724268 (English).
- ↑ Tsung-Dao Lee and Michael Nauenberg: Degenerate Systems and Mass Singularities . In: Physical Review D . tape 133 , 6B, 1964, pp. B1549 - B1562 , doi : 10.1103 / PhysRev.133.B1549 (English).
- ^ Taizo Muta: Foundations of Quantum Chromodynamics . 3. Edition. World Scientific, 2010, ISBN 978-981-279-353-9 , pp. 345 ff . (English).