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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Is there somesort of “recipe” to check if an spacetime exibit the Unruh effect?

Firstly I don't know for sure if this question makes a solid sense, concerning the physical phenomena. I) Unruh Effect Now, we have then the Unruh effect which appears just by considering the ...
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Reference for Quantum field theory in $S^1 \times R$

I am looking for a reference where it is considered QFT on a space given in a circle, plus a time coordinate, namely QFT in $S^1\times R$.
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Bogoliubov coefficient (not) being equal to zero

When discussing the nature and ambiguity of particles in curved space-times, one usually ends up at an expression for annihilation/creation operators that looks something like: $$ a_{i}=\sum_{j}(\...
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Why choosing l=0 density when calculating the free energy on curved spacetime

I am doing a research in counting the micro states in field theory, and I find when it reduces to the eigenvalue problem of Laplacian in Homogeneous space $\mathbb{H}^d$, people choose the state ...
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What is an vacuum in QFT in curved spacetime?

Sometimes in some public lectures about General Relativity (GR) and Quantum Mechanics, in college, the professors dealt with the vacuum concept, precisely in the context of Quantum Field Theory (QFT), ...
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'Gauge invariant phase' - KG equation with EM potential in Hawking radiation

Given the massless scalar electromagnetism equation $$g^{ab}(\nabla_a -ie A_a)(\nabla_b -ie A_b)\phi=0, \quad \quad \quad \quad(3.5)$$ I include the following passage from Hawking's "Particle ...
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geodesic equation for electromagnetic field

I am trying to derive geodesic motion for photons from the Lagrangian of electromagnetism coupled to General Relativity. I tried to use the covariant conservation of the Stress energy tensor: $$\...
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Fourier transform in Hawking's paper

While calculating $\beta_{ij}$ for the case of a Schwarzschild black hole, Hawking uses the Fourier transform of the solution of the wave equation (Particle Creation by Black Holes, S.W. Hawking, ...
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How does the connection of constant-phase surface in Schwarzschild spacetime work?

I am stuck while following the calculation of constant-phase surface of Hawking radiation in Hawking's original paper (Particle Creation by Black Holes, S.W. Hawking, Commun. Math. Phys. 43, 199 (1975)...
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Opposite of Particle Creation in QFT in curved spacetime

I know that in Quantum Field Theory in curved spacetime particle creation is possible. My question is whether the opposite "particle vanishing" is also possible? I don't like to use the word particle ...
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Do virtual photons follow spacetime curvature?

I have read this question: https://link.springer.com/chapter/10.1007%2F978-3-319-13443-7_26 The electric field lines from a point charge — and the rays of light when the charge is replaced by a ...
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Feynman diagram for Hawking radiation?

I'm starting to wrap my head around Feynman diagrams, and the idea of "real" vs. "virtual" particles, but one area where this distinction seems to break down is in describing Hawking radiation, where ...
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Difference between QFT In curved spacetime, semiclassical, and quantum gravity?

Could someone describe the difference, qualitatively, between QFT in curved spacetime, semiclassical gravity, and quantum gravity? I know that each is an approximation to the next and the end goal is ...
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Evaporation of large charged black holes

Black holes evaporate (Hawking Radiation) acting as black bodies with the temperature inversely proportional to the mass. No physical process, be it evaporation or any other "trick", can make a black ...
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Derivation of the spin connection in curved spacetime

I am trying to understand the derivation of spin connection from the book "Quantum Field theory in Curved spacetime" by L. Parker and D. Toms. In chapter 5, page 223, they have written (which I am ...
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Definition of vacuum in Schwarzchild metric

There are three possible choices of vacuum in the literature for a spherically symmetric black hole with the geometry defined by the Schwarzschild metric. The choices are: a) Boulware vacuum. b) ...
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What quantum effects that involve gravity can be studied without stuff like QFT or string theory?

So there is no a full quantum theory of gravitation. However, there are instances where quantum effects due to gravitation have been studied. Like Gravitational neutron interferometry https://arxiv....
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Hawking-Hartle vacuum in Hamiltonian formulation

In a spacetime with a bifurcate Killing horizon, one can use the Killing vector on one side of the horizon to prepare a smooth global state across it, by performing a Euclidean path integral to the ...
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Are the field equations describing quantum fields in a curved space time generally co-variant in the same sense as classical field equations?

I have seen in many references that the field equations for a quantum field in curved space time is mentioned to be 'manifestly co-variant'. The procedure that has been followed to arrive at these ...
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Unitary equivalence of two representations

Suppose we make a transformation from Minkowski space to another coordinate system. What does it mean to say that the two spaces are unitarily equivalent? I have often seen the comment that if the ...
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Are Bremsstrahlung and the Unruh effect equivalent?

This paper argues that the absorption and emission rates from and to the thermal Unruh bath of a proton viewed in a coaccelerated frame is equal to the emission rated viewed from an inertial observer. ...
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What are zero-energy Rindler photons?

In the discussion of the Unruh effect and Bremsstrahlung (e.g. here) I always come across "zero-energy Rindler photons". What exactly are these? Shouldn't a zero-energy photon correspond to a static ...
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The idea behind the geometrical description of a closed curved space

This question is about the idea of how to describe a curved space, I'm not asking for formulas because I've never studied this topic before. Let's imagine an ant on a sphere, it will use two ...
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Dirac equation in curved spacetime

As we know, the laws of physics in curved spacetime are obtained to lowest order by upgrading the flat space laws by substituting partial derivatives with the appropriate covariant derivatives. In the ...
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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 ...