# Quantum Electrodynamics in Curved Spacetime

• paweld
In summary: There have been some attempts, but they are much more difficult than in flat backgrounds. I would recommend looking into books like "QFT on Curved Spacetime and Black Hole Thermodynamics" by Wald or "QFT in Curved Spacetime" by Birrel, Davies. They both have descriptions of how to quantize a scalar noninteracting Klein-Gordon field on a curved manifold. There is also a paper "Perturbative QFT on Curved Backgrounds" by Chandrasekhar et al. which gives a more general introduction to perturbative QFT on curved backgrounds.
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?

paweld said:
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

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.

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

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.

paweld said:
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.

Last edited by a moderator:

## 1. What is quantum electrodynamics in curved spacetime?

Quantum electrodynamics in curved spacetime is a theory that combines the principles of quantum mechanics and general relativity to describe the behavior of electromagnetic fields in the presence of curved spacetime. It is an essential part of understanding the fundamental interactions between matter and light in the universe.

## 2. How does quantum electrodynamics in curved spacetime differ from regular quantum electrodynamics?

In regular quantum electrodynamics, the spacetime is assumed to be flat and the effects of gravity are not considered. In quantum electrodynamics in curved spacetime, the effects of gravity are taken into account, and the spacetime is described as having a curvature due to the presence of massive objects.

## 3. What are the applications of quantum electrodynamics in curved spacetime?

Quantum electrodynamics in curved spacetime has numerous applications in modern physics, including the study of black holes, the early universe, and the behavior of particles in extreme gravitational fields. It is also used in the development of theories such as quantum gravity and the search for a unified theory of all fundamental forces.

## 4. What are the key concepts in quantum electrodynamics in curved spacetime?

The key concepts in quantum electrodynamics in curved spacetime include the quantization of the electromagnetic field, the effects of spacetime curvature on the behavior of particles, and the renormalization of divergent calculations. Other important concepts include vacuum fluctuations, virtual particles, and the use of Feynman diagrams to calculate interactions between particles.

## 5. What are the challenges in studying quantum electrodynamics in curved spacetime?

One of the main challenges in studying quantum electrodynamics in curved spacetime is the complexity of the mathematical calculations involved. The theory also faces conceptual challenges, such as the question of how to reconcile it with other theories, like general relativity. Additionally, the lack of experimental evidence for some of the predictions of the theory makes it difficult to fully test and validate its predictions.

• Quantum Physics
Replies
6
Views
695
• Quantum Physics
Replies
4
Views
672
• Quantum Physics
Replies
6
Views
398
• Quantum Physics
Replies
25
Views
2K
• Quantum Physics
Replies
6
Views
1K
• Quantum Physics
Replies
3
Views
909
• Quantum Physics
Replies
134
Views
7K
• Quantum Physics
Replies
141
Views
10K
• Quantum Physics
Replies
6
Views
649
• Quantum Physics
Replies
3
Views
2K