X-Message-Number: 22030 From: "michaelprice" <> References: <> Subject: Infrared divergence Date: Thu, 19 Jun 2003 18:28:21 +0100 Yvan Bozzonetti: >> When a charge is accelerated the low-frequency energy of the >> Bremsstrahlung radiation emitted is independent of frequency, >> so that the number of low energy photons emitted scales with the >> inverse of the frequency. Total photon number is obtained by >> integration of the inverse function to yield the logarithmic function. >> Since log(0) = infinity we have an infinite number of low-energy >> or "soft" photons, even though the total energy emitted is finite. >> > I disagree :-( > The real acceleration takes place in a finite time T, Photons with > period (inverse of the frequency) far larger than T can't be > radiated away. they remain as virtual photons. The magnitude and period, T, of the acceleration affects the utraviolet (high-frequency) nature of the radiation, rather than the infrared or low-frequency end of the spectrum. > So, the number of > photons, real + virtual is indeed infinite, but the number of real > ones is finite. The infinite photon problem is an artifact coming > from using a classical idea (instantaneous photon production) > in a quantum problem. > According the quantum field theory the number of virtual *and* real photons emitted during Bremsstrahlung are *both* infinite. See, for instance, Appendix 6 (Infrared Divergences to All Orders) of Quantum Field Theory by Michio Kaku, which is quite explicit on this point. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=22030