- #1

paweld

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If yes could you give me some references to papers in which solution

to these problem is described?

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- Thread starter paweld
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- #1

paweld

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If yes could you give me some references to papers in which solution

to these problem is described?

- #2

A. Neumaier

Science Advisor

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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

- #3

paweld

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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.

- #4

DarMM

Science Advisor

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I can answer your question, but first I must ask what you mean by "the formalism

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.

of QFT on curved spacetime". The answer will depend on this.

- #5

paweld

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"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.

- #6

DarMM

Science Advisor

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

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" [Broken]

Perturbative QFT is much more difficult in curved backgrounds.

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