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| Jay R. Yablon... |
 Posted: Fri Oct 30, 2009 8:10 am |
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Guest
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In the file linked below, I have laid out an exercise upon which I would
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 (3.3 )
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: jyablon at (no spam) nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.roadrunner.com/~jry/FermionMass.htm |
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