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