Looking for Feedback on an Exercise Calculating the QED Path Integral and Green's Functions in Curved Spacetime with Boundary Terms
Jay R. Yablon
appreciate your feedback:
http://jayryablon.files.wordpress.com/2009/10/path-integration-of-the-maxwell-action-2-4.pdf
Basically, I am attempting in the three respective sections of this
exercise to:
1) Integrate-by-parts, the classical electrodynamic action, in curved
spacetime, retaining the boundary term (a suggestion earlier made by M.
Hopkins). (The result is equation (1.10))
2) Quantize this action, using the Path Integral method. (The result is
equation (2.15))
3) Apply the Wick method of successive differentiation, to develop the
Green's functions for QED in curved spacetime, with the boundary term
included in, and indeed integral to, this calculation. (This result is
in equation (3.38))
I have done all of this spacetime, and not yet attempted any conversions
over into momentum space, recognizing that this is seen to be
problematic in curved spacetime. Thus, I felt it prudent to push this
development as far as possible without yet crossing the bridge of how
one carries out harmonic analysis (the analog of Fourier analysis) in
curved spacetime. (See a related thread on this topic, titled "What
Happens to Fourier Transforms in Curved Spacetime?")
My next step is to tackle the question of harmonic analysis in curved
spacetime, and the above development establishes the context within
which I am motivated to consider this question.
I would like at this point, to know if I am more or less doing the right
things so far.
Thanks,
Jay
____________________________
Jay R. Yablon
Email: jya...@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.roadrunner.com/~jry/FermionMass.htm
Mike
> My next step is to tackle the question of harmonic analysis in curved
> spacetime, and the above development establishes the context within
> which I am motivated to consider this question.
>
Are you aware of the work of Hagen Kleinert? He has some chapters on
path integrals in curved spacetime.
"harmonic analysis", you say? It sounds like you're thinking about
particles in curved spacetime. Are you aware that it is suppose to be
impossible to get particles to appear in curved spacetime formulations?
Ken S. Tucker
> In the file linked below, I have laid out an exercise upon which I would
> appreciate your feedback:
>
> co-moderator: sci.physics.foundations
> Weblog:http://jayryablon.wordpress.com/
> Web Site:http://home.roadrunner.com/~jry/FermionMass.htm
We study signal analysis to improve our products,
for your pleasure run the loons WAV or ASF from here,
http://www.trak4.com/earco/index.html
Was that digitized from analog !?!
Obviously we convert acoustics to electronic current.
What I understand is 'power' (W) is quantized, so if we were
to slow time, an acoustic signal would be converted to clicks,
even in electromagnetic relations moving electons via photons,
as an acoustic signal is transmitted by wire, so at a basic
level the Fourier Transform is subsumed into an arithmetic.
I suppose there is pedological considerations by using the
Fourier, but in the 'down and dirty' basics of physics, we're
pushing and pulling electrons (molecules) via photonics.
I'm suggesting an AC current (acoustics) as it's familiar,
that is done with air, wire or fiber optics.
Regards
Ken S. Tucker
Ken S. Tucker
> Was that digitized from analog !?!
> Obviously we convert acoustics to electronic current.
>
> What I understand is 'power' (W) is quantized, so if we were
> to slow time, an acoustic signal would be converted to clicks,
> even in electromagnetic relations moving electons via photons,
> as an acoustic signal is transmitted by wire, so at a basic
> level the Fourier Transform is subsumed into an arithmetic.
>
> I suppose there is pedological considerations by using the
> Fourier, but in the 'down and dirty' basics of physics, we're
> pushing and pulling electrons (molecules) via photonics.
>
> I'm suggesting an AC current (acoustics) as it's familiar,
> that is done with air, wire or fiber optics.
> Regards
> Ken S. Tucker
Hi Jay et al,
Being tecky I try to get an apparatus to wrap my mind around.
I'll set-up a Vertical transmitter antenna of length L, with differing
gravitational potentials at the top and bottom, the boundary is L.
An A/C current (transmisssion frequency) is fed in at the bottom.
The conduction along the antenna is QE Dynamically as the e-
(electrons) are pushed and pulled by repulsion and attraction,
and that 'action' is quantized.
What wave equation (that departs from a pure sine) results as
the gravitational potentials are varied?
Is that a proper formulation of an exercise?
Since the apparatus exists, experimental capacity follows.
I think we could get down to the electron level, Pound-Rebka
was very clever.
Regards
Ken S. Tucker