Re: massless or massive photon?
- From: Igor <thoovler@xxxxxxxxxx>
- Date: Wed, 9 Jul 2008 17:21:20 -0700 (PDT)
On Jul 8, 9:11 am, "Juan R." González-Álvarez
<juanREM...@xxxxxxxxxxxxxxxxxxxx> wrote:
The usual argument for massless photons uses the Hamiltonian
H = (\sqrt (m^2c^4 + p^2c^2) ) (1)
and set (m = 0) to yield
H = pc
However, the original Hamiltonian (1) was derived using the Legendre
transformation
H = pv - L = (\sqrt (m^2c^4 + p^2c^2) )
If alternatively we start assuming (v = c) in the transformation, the
result is
H = pc - L = pc (2)
where no assumption was taken about the mass.
Is this Hamiltonian (2) representing some kind of massive photon (somewhat
as in Proca theory [#]) or is really the same that (1)?
[#]http://en.wikipedia.org/wiki/Proca_action
--
Center for CANONICAL |SCIENCE) http://canonicalscience.org
As I've always understood it, the assignment of v = c as a special
case should only occur AFTER the Legendre tranform has been
performed. I think in this particular case, you get the correct
result coincidently. But in general that probably wouldn't happen.
Besides, the Lagrangian in the wiki link you've provided is a field
Lagrangian density, whereas the analysis you've provided entails a
mechanical Lagrangian. They're entirely different animals.
.
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