Quantum Electrodynamics in Curved Spacetime

[paweld]

Does anyone know if there exist a formulation of QED in curved spacetime.
If yes could you give me some references to papers in which solution
to these problem is described?

 

[A. Neumaier]

Does anyone know if there exist a formulation of QED in curved spacetime.
If yes could you give me some references to papers in which solution
to these problem is described?

see, e.g., http://arxiv.org/pdf/0906.3837

 

[paweld]

Thanks. This paper show how to compute some correction to QED which arises
as a result of nonflat background metric. Are there any any attempts to formulate
QED on a classically described curved background from the beginig using the formalism
of QFT on curved spacetime.

 

[DarMM]

Thanks. This paper show how to compute some correction to QED which arises
as a result of nonflat background metric. Are there any any attempts to formulate
QED on a classically described curved background from the beginig using the formalism
of QFT on curved spacetime.

I can answer your question, but first I must ask what you mean by "the formalism
of QFT on curved spacetime". The answer will depend on this.

 

[paweld]

By the formalism of QFT on curved spacetime I mean theory which is presented in book
"QFT on curved spacetime and black hole thermodynamic" by Wald or "QFT
in curved spacetime" by Birrel, Davies. They state procedure how to quantize scalar
noninteracting Klein-Gordon field on curved manifold (in breif: one can find a
"complete" set of solution of Klein-Gordon eq which in general are not plane waves
and write the field as a combination of these solution; coefficients which appear
in this decomposition are creation and anihilation; the division on positive and
negative solution of KG eq. is not unambiguous; different divisins often lead to
Hilbert spaces which are not unitarly equivalent; Wald describes also algebraic
approach to QFT in CS which is more mathematically rigorous). I know that
it is possible to quantize in this manner free Dirac and electromagnetic field.
I wonder if anybody tried to treat realistic interacting fileds in this approach.

 

[DarMM]

By the formalism of QFT on curved spacetime I mean theory which is presented in book
"QFT on curved spacetime and black hole thermodynamic" by Wald or "QFT
in curved spacetime" by Birrel, Davies...

No, QED cannot be treated that way since it is interacting.

However since those methods give rise to a good construction of free fields they allow you to perform perturbation theory in curved spacetime, just as easily as you could perform it in flat spacetime. In fact a renormalizable theory in flat spacetime can be shown to be renormalizable in curved spacetime.

So one can treat perturbative QED on curved backgrounds. For an introduction to what is involved, but simplified for the scalar case try:
http://arxiv.org/abs/math-ph/9903028"

Perturbative QFT is much more difficult in curved backgrounds.