# Solving Ambiguity in QFT in Curved Spacetime

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• fxdung
In summary, the conversation discusses the issue of non-uniqueness in the motion equation derived from field theory in General Relativity, and how this ambiguity can be solved by requiring spacetimes to be globally hyperbolic in the classical theory. The question of what specific non-uniqueness is being referred to is unclear, and the conversation ends with a request for the equations in question to be provided.
fxdung
I know that motion equation in field theory deriving in GR is not uniquely.How do we solve this ambiguousness of QFT in curved spcetime?

In the classical theory, one way is to also require the condition that spacetimes be globally hyperbolic.

It isn't very clear what the question is. What non-uniqueness are you reffering to?

Eg, we can have two forms of Klein-Gordon equation of scalar field in GR,

fxdung said:
we can have two forms of Klein-Gordon equation of scalar field in GR,

Can you write them down?

See page70 General Relativity of Wald.

fxdung said:
See page70 General Relativity of Wald.

## 1. What is QFT in curved spacetime?

Quantum field theory (QFT) is a theoretical framework that combines quantum mechanics and special relativity to describe the behavior of particles at a microscopic level. In curved spacetime, the framework is extended to include the effects of gravity, as described by Einstein's theory of general relativity.

## 2. What is ambiguity in QFT in curved spacetime?

Ambiguity in QFT in curved spacetime refers to the fact that there is no unique way to define the theory. This is due to the mathematical difficulties of combining quantum mechanics and general relativity, which leads to different possible interpretations and formulations of the theory.

## 3. Why is solving ambiguity in QFT in curved spacetime important?

Solving ambiguity in QFT in curved spacetime is important because it allows us to have a better understanding of the fundamental laws of nature. It also helps us to make more accurate predictions and calculations in situations where both quantum mechanics and gravity are relevant, such as in the early universe or around black holes.

## 4. How do scientists approach solving ambiguity in QFT in curved spacetime?

Scientists use a variety of mathematical and theoretical tools to try and resolve the ambiguity in QFT in curved spacetime. This can include using different mathematical frameworks, such as perturbation theory or renormalization, and incorporating new concepts such as supersymmetry or string theory.

## 5. What are some current challenges in solving ambiguity in QFT in curved spacetime?

Some of the current challenges in solving ambiguity in QFT in curved spacetime include finding a consistent and mathematically rigorous way to combine quantum mechanics and general relativity, as well as reconciling different approaches and interpretations of the theory. Additionally, there is still much to be explored and understood about the behavior of particles in extreme conditions such as those found near black holes or during the early stages of the universe.

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