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Questions tagged [qft-in-curved-spacetime]

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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Hawking radiation doubt [duplicate]

My question is that according to hawking radiation two particles pop near a black hole one goes into the black hole and one escapes from it so we get the impression that the black hole is radiating ...
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Rigorous plane wave expansion in QFT

I work with quantum field theory in curved spacetimes, so I'm not fully aware of the notation used in standard QFT. However, I'll try to make myself clear. In standard QFT, the one-particle Hilbert ...
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Hawking radiation of massive scalar field

There are some calculations about Hawking radiation (expectation value of particle number operator, 2-point function, stress-energy tensor, and so on.), which are often done under the condition that ...
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How to calculate $n$-point functions of interacting fields in curved spacetime (Schwarzschild metric)?

How to renormalize quantum field theory in curved spacetime? (or in Schwarzschild spacetime?)  I want to calculate n-point functions $$<0|Tφ(x_1)...φ(x_n)|0>$$ in massless $φ^4$ theory in ...
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Particle decoupling, universe expansion and QFT

A particle (say neutrino) decouples from the plasma in the early universe when its interaction rate $\Gamma$, with the plasma, is slower than the expansion rate $=H = \frac{\dot{a}}{a}$, i.e. $\Gamma &...
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quantum fluctuations at the horizon

So suppose we have a black hole with hair, that is a background solution in our field theory that describes a black hole spacetime and in which a field coupled to gravity has a non zero configuration. ...
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Notation for the vector space of (real) classical solutions

I am aware that this might not be the best place to ask, but I can't say I know of any other better alternative so I apologize in advance. I'm following Wald's book on QFT in curved space-time and I ...
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Origin of $\sqrt{-g}$ in the integral of action $S$

I have a question that might (and probably will) be stupid: I do not understand where does the factor $\sqrt{-g}$ (i.e. $\sqrt{-\det\left(g_{\mu\nu}\right)}$) come from in the action integral S when ...
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Is the partial derivative in the Dirac equation in curved space contracted with a tetrad?

The Dirac Equation in Curved spacetime makes a difference between Lorentzian indicies and Covariant indicies. In the equation we find a $\partial_\mu$. Is this actually $e^a_\mu\partial_a$ where $e$ ...
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Momentum Operator in curved spacetime (QFT)

In flat space we have $$\hat{p}_\mu=-i\hbar \partial_\mu . $$ Does this still hold in a curved spacetime (particularly Schwarzschild space)?
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Derivation of Covariant derivative for fermionic fields

I've been reading about the Dirac equation in curved spacetime and understand the nature of the verbien, but am wondering what the relationship is between the two definitions of the Fermionic ...
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How do fermions explicitly interact with curvature via the tetrad?

I am aware of the basics of the tetrad formalism and am clear on why bosonic fields do not have couplings to curvature via their covariant derivatives in a curved space Lagrangian i.e. why $\nabla_\mu\...
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Black hole horizon states in standard derivations of Hawking Radiation

In all standard derivations of Hawking radiation given e.g. by Hawking, Parker and Wald, one has the so-called horizon states. The point is that when one is quantizing a scalar field on a black hole ...
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How does the spin connection affect the dynamics of a fermion in curved space?

Consider a massless right-handed Majorana fermion in curved spacetime. Without any other fields present, the Lagrangian density is (I believe) the following: $$ \mathcal{L}_{\psi} = \sqrt{g}i\bar{\...
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Is the Klein-Gordon equation one evolution equation for states?

I remember when first studying relativistic QM that it was argued that viewing the Klein-Gordon equation as one evolution equation for a state like the Schrodinger equation leads to some issues. This ...
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Can a proton and an electron annihilate in a gravitational field?

According to this Physics.SE comment, it is gravitationally allowed, though very unlikely, for a proton and an electron to annihilate yielding two photons. Is that correct? If so, why? (In ...
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Simple Hamiltonian in curved space-time

Consider the theory of a free massless scalar field with a non-trivial background metric: $$ \mathcal{L} = -\sqrt{-g} \left( \frac{1}{2}\partial_\mu \phi \partial^\mu\phi\right) .$$ (I prefer the '...
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Why is this the probability that an incoming wavepacket is absorbed by the black hole?

I'm reading Parker's book "Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity" and when talking about Hawking radiation, there's a claim that I've not been able to understand. He ...
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How to interpret this construction of the states in QFT?

Non-Relativistic Quantum Mechanics To make this question clear it might be useful to contrast with non-relativistic quantum mechanics. In any quantum theory, the states of a system are unit rays in ...
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Kinetic term for a Majorana fermion in curved Weyl geometry

I am trying to write the action for a Majorana fermion on a curved Weyl-gravity background. Since I am considering a fermion in curved space, the tetrad formalism is appropriate and the kinetic term ...
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Is there a connection between these two results on soft hair on black holes?

In 2016 Strominger, Hawking and Perry published the paper "Soft Hair on Black Holes" proposing new results that could have importance to the study of the black hole information problem. One ...
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Respect to What Time is Calculated in Space

This may be the silly and stupid question but I have read that time appears to move slower near massive objects because the object's gravitational force bends space-time and the phenomenon is called ...
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Where this interpretation for the field modes comes from?

I'm reading the book "Modeling Black Hole Evaporation" by Alessandro Fabbri and Jose Navarro-Salas, and in section 3.3.2 they talk about wavepackets at $\mathscr{I}^+$. It all starts like this: one ...
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Should the parallel propagator appear in the point-split stress-energy tensor?

The first step in Hadamard regularization of the stress-energy tensor of a free Dirac field is to write out the point-split expression $$\langle T_{\mu \nu} \rangle \equiv \frac{1}{4} \lim_{x'\to x} \...
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Running coupling constants within a highly compressed object

I wonder is it possible. in highly compressed objects, such as neutron stars and black holes, (I'm not sure that this applies to singularities), that the physical conditions within these objects ...
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What's the problem with Black Hole evaporation?

Black hole evaporation is not unitary because it takes a pure state to a mixed state. On the other hand, ordinary decay processes in Quantum Mechanics do not seem very unitary either. (For example, if ...
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Is it possible to define Feynman diagrams in curved space-time?

I have a very simple question: "Is it possible to talk about Amplitudes and Feynman diagrams assuming a different background than the usual Minkowski one? Let's assume for example that the background ...
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1answer
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How to fuse quantum mechanics and general relativity?

I am very new to this topic but I have started reading Kevin Wray's lecture notes about string theory (PDF) and in the introduction he says: "Sometimes it is said that we don’t understand how to ...
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Quantum Mechanical amplitude for particle falling into a black hole

Consider a black hole spacetime originated by gravitational collapse, like the following Vaidya geometry $$ds^2=-\left(1-\frac{2M\theta(v)}{r}\right)dv^2+2dvdr+r^2(d\theta^2+\sin^2\theta d\phi^2).$$ ...
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Hawking Radiation from a Physical Black Hole

For distant observer, a physical black hole takes an infinite amount of time collapse, because time is redshifted near the Schwarzchild radius. Instead of the matter crossing the horizon, it will just ...
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2answers
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How do you derive a quantum field theory from a spacetime metric?

What are the first steps in converting a metric into a quantum field theory? I know roughly what to do once I have a pair of non-commuting operators, but how do I get to that point? Specifically, I'd ...
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“Hadamard” divergences for interacting theories

When dealing with noninteracting theories on potentially-curved manifolds, one can define e.g. quadratic operators, which formally diverge, using the ``Hadamard" regularization procedure. One central ...
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Hadamard regularization boundary condition

I am working through the Hadamard regularization of two-point functions of scalar fields in curved spacetime in 2D e.g. equations 26 and 33-36 in https://arxiv.org/pdf/gr-qc/0512118v2.pdf. The idea ...
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Does thermal state in Rindler spacetime correspond to Minkowski vacuum?

We know that the Minkowski vacuum corresponds to the thermal state in a Rindler wedge at Unruh temp. But does the thermal state in one Rindler wedge at Unruh temperature uniquely map to the Minkowski ...
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Temperature due to the cosmological horizon during inflation

During inflation, the de Sitter space has a cosmological event horizon. This horizon exists because farther than the horizon distance the expansion carries light away from the observer faster than the ...
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What if the usual predictability of the laws of physics fail in general relativity?

In Newtonian mechanics the future is predictable, If we know the initial state of a system exactly, then the laws of physics determine its state arbitrarily far into the future. What if the usual ...
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How can both horizon and outgoing modes be kept together in this state if evaporation eliminates the horizon?

In the original computation of Hawking radiation one starts with a gravitational collapse spacetime (like the Vaidya geometry with $M(v)=M_0\theta(v-v_0)$). Then one introduces three complete sets of ...
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Is energy conserved in QFT in curved spacetime?

Energy is conserved in QFT in flat spacetime. Does energy conservation still hold in QFT in curved spacetime? I already searched this site and google about this but didn’t find a clear answer
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How do Feynman diagrams and loop quantum gravity fit together?

Feynman diagrams are a good way of calculating effects in quantum electrodynamics on a constant background space-time. Spin foams (LQG) are conjectured to be a good way of calculating quantum effects ...
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Interacting Quantum Fields in Curved Spacetime

I was thinking this night that how would the fields interaction or the vacuum expectation value of Higgs field changes when spacetime is not flat? e.g., the higgs field interact with the electron ...
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Mathematical formulation of density matrix on hypersurface in 3+1 formalism

Of course we have a notion of qft in curved spacetime, though I'm not sure how one can represent a particle state on curved spacetime without a timelike Killing vector field (i.e. a particle should ...
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Why do we need these two sets of modes in the gravitational collapse?

Consider the gravitational collapse spacetime: Hawking argues in his paper$^{[1]}$ about black hole radiation that the massless scalar field $\phi$ can be decomposed as $$\phi = \sum_i \{p_i b_i+...
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Why is it impossible to formulate unitary QFT in a dynamical background?

I cannot recall the exact argument but I remember my professor saying something like unitary time evolution in a dynamical background "kicks" a state out of the Hilbert space constructed on curved ...
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Experimental tests of QFT in curved spacetime

In terms of QFT in curved spacetime (qftics), are there any known tests that confirm/void it to be a correct prescription for a first order approximation quantum theory of gravity? Obviously the ...
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What is meant by the multi-particle state $|n\rangle^{(+)}$ here?

I am reading Takagi's paper `Vacuum noise and stress induced by uniform accelerator'. I will attach a screenshot of something I am confused about (from page 31). I have a simple question: what is ...
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How to understand Hawking's interpretation of the quantization of the field?

In Hawking's paper "Particle Creation by Black Holes" he says the following: The operator $\phi$ can be expressed as $$\phi=\sum_i f_i a_i+\bar{f}_ia_i^\dagger.$$ The solutions $\{f_i\}$ of ...
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Re-expressing the Lorenz gauge condition in terms of the Faraday tensor (in curved spacetime)

I was wondering if the equation $\nabla_\mu A^\mu = 0$ could be written as a constraint equation solely on the $F_{\mu \nu}$ components. It seemed like the bulk of the problem was isolating terms such ...
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Rindler-Fulling Quantization - Rindler mode expansion of $\phi$: why are we ignoring the Past and Future Wedges?

I am following along Chapter 2 of Takagi's Vacuum noise and stress induced by uniform accelerator. I am at the point of performing the Rindler-Fulling Quantization of a real scalar field, where you ...
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Why is $K \cdot T$ a conserved vector?

I am following along Chapter 2 of Takagi's Vacuum Noise and Stress Induced by Uniform Acceleration. For a free real scalar field $\phi$ the stress-energy tensor is: $$ T_{\mu\nu} = ( \partial_{\mu} \...
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Solving the KG equation in Rindler coordinates

Let us consider a massive Klein-Gordon scalar field $\phi$ satisfying $$(\Box+m^2)\phi=0$$ I want to solve this in Rindler coordinates, choosing $\phi$ to be positive frequency with respect to the ...