Quantum field theory (QFT) in curved spacetime is a field of study that focuses on problems that arise when considering a quantum field on a fixed, curved spacetime.

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Evidence for electrodynamics in curved spacetime

Field theories in curved spacetime is usually formulated by integrating their Lagrangian over the curved spacetime. For example, for electrodynamics, we have the action $$ S = \int d^4x \left( ...
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Energy and momentum conservation - why it is so fundamental?

Over hundreds of years the conservation of energy and momentum in a closed System was proven. 100 years ago, Emmy Noether showed that these fundamental laws arise from the following facts and vice ...
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59 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
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Can we test QFT on a curved spacetime?

It is possible to extend a quantum field theory to a curved spacetime. But does this lead to predictions that can be tested and measured? Had it been confirmed? The underlying reason I am asking this ...
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How to prove explicitly that by including Dirac fermions into the Einstein-Hilbert action we make torsion to be non-zero?

Recently I've heard the statement that by including Dirac fermions into the Einstein-Hilbert action we make torsion be non-zero, so that is one of problem of quantum gravity. How to prove that ...
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Why gamma-matrices are associated with tetrads Lorentz rotation?

In Zee's "QFT in nutshell" in a paragraph "Differential geometry of Riemann manifold" he states that Dirac gamma-matrices are associated with tetrads Lorentz rotation, so Dirac lagrangian in curved ...
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What's the physical or mathematical meaning of considering non-minimal coupling?

Why we still consider the case of non-minimal coupling? And I don't really understand the motivation of coupling. In general relativity, the non-minimal coupling violates the principle of ...
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How would gravitons couple to the Stress-Energy tensor?

How would gravitons couple to the Stress-Energy tensor $T^{\mu\nu}$? How did physicists arrive at this result? I've read that it follows from the analysis of irreducible representations of the ...
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Intuition behind $U(1)$-gauge model of Electrodynamics in a general spacetime

As the article Electrodynamics in general spacetime greatly explains, the $U(1)$-gauge theory is a good base for working in non-simply connected spaces. But I wonder whether there is a deep reason to ...
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Isolating the divergences in the stress energy tensor

In DeWitt's report "Quantum Field Theory in Curved Spacetime" (B. S. DeWitt, Phys. Rep. 19C, 292 (1975)), he states that in Eq.(175) $$\langle in, vac| T^{\mu\nu}|in,vac\rangle = 2 \frac{\delta ...
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Background field expansion in normal coordinates

Background field expansion following form $Y= X+\pi$ where $X$ is my background field and $\pi$ is the fluctuation. From the Normal coordinates we have the expansion of $\pi^{\mu} = ...
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Diffeomorphisms and the Dirac action

I have a question concerning fermions in curved space-time. Please read it to the end before suggesting the spin-connection and vierbein-based approach. I heard that there is a special way of ...
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Electric charges on compact four-manifolds

Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
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Does Hawking radiation need an apparent horizon and when does it switch on during stellar collapse?

I've read that Hawking radiation is implicitly linked with the existence of an apparent horizon (1). This seems a slightly less onerous than linking Hawking radiation with a genuine bona fide event ...
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202 views

Wick Rotation in Curved space

So over time I have learned to do exhaustive searches before asking things here. Wick rotations are cool if you are trying to work in qft and make statements about the thermodynamics of some physical ...
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How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
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What's the conserved quantities correspond to the generator of conformal transformation

What's the conserved quantity corresponding to the generator of conformal transformations?
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227 views

Normal ordering in curved spacetime

In the flat spacetime, one can perform normal-ordering to set the energy of the vacuum state to zero. I read in some places that this procedure cannot be consistently performed in the curved ...
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Solving electromagnetic vector field using the Lagrangian

Given an action of the form \begin{equation}S=-\frac{1}{4}\int d^4x\eta^{\mu\nu}\eta^{\lambda\rho}F_{\mu\lambda}F_{\nu\rho}\end{equation} where ...
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Gauge invariance of Rarita-Schwinger action in curved spacetime

The Rarita-Schwinger action in curved $n$-dimensional spacetime is $$ \int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c $$ Here $g = \det(g_{\mu \nu})$, and the indices $a, b \dots$ are ...
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Dirac equation in curved spacetime - found second derivatives of the metric, violation of the principle of equivalence?

I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the ...
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437 views

Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
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QFT in curved space [closed]

Can someone exactly tell me what one gains from doing QFT in curved space, and how reliable these new results are. I want to know if it is worth while putting some man hours towards this. Please ...
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Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
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Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
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637 views

Minimal vs. Non-minimal coupling in General Relativity

What is the difference between Minimal vs. Non-minimal coupling in General Relativity? A brief introduction to Minimal Coupling in General Relativity could be useful too.
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Getting the Lagrangian from the action in curved spacetime

Suppose I have this action: $$ S = \int \mathrm d^4 x\sqrt{-g}\times \text{something}$$ where $g$ is the determinant of the metric. Should I take the Lagrangian to be: $$ \mathcal L = \sqrt{-g} ...
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271 views

Dirac Lagrangian density in curved spacetime

I'm trying to derive this form of the Dirac Lagrangian density in curved space-time: $$ \mathcal{L}~=~\det\left(e\right)\bar{\Psi}\Bigg ...
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Is a QFT in a classical curved spacetime background a self-consistent theory?

EDIT: Better rewording by Chris White: Is it possible to have a theory that treats both GR and QFT (e.g. QFT on a curved spacetime dynamically influenced by the standard QFT fields)? Is such a theory ...
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616 views

Scalar field lagrangian in curved spacetime

I am studying inflation theory for a scalar field $\phi$ in curved spacetime. I want to obtain Euler-Lagrange equations for the action: $$ I\left[\phi\right] = \int ...
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247 views

Massless fields in curved spacetimes

I read the following statement in one of Penrose's paper zero rest-mass field equations can, with suitable interpretations, be regarded as being conformally invariant. I take this to imply that ...
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115 views

Two definitions: 'semi-classical space-time' and 'supersymmetric Minkowski space'

By reading articles I ran several times into two terms, never being defined so I assume they must have well established definitions somewhere. The first is semi-classical space-time. If I where to ...
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General Relativity research and QFT in curved spacetime

A naive question: Are these subjects, i.e. classical GR and QFT in curved spacetime, being worked upon much anymore? Who is researching this and what are the problems within these fields? Any ...
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Why is Dirac Lagrangian in Curved Spacetime Weyl Invariant?

Are there any references on the Weyl invariance of the Dirac Lagragian in general spacetime?