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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Lattice QFT: Non-homogenous lattice spacing

I am interested why we fix the lattice spacing, $a$ to be homogenous in all dimensions. After a Wick rotation, $a=i \epsilon$ where $\epsilon=t_{i+1} - t_{i}$ and with euclidean time given by $\tau = ...
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How to calculate the free energy in curved space?

To study the Hagedorn temperature of string near a black hole, we need to calculate the free energy in curved space. This is can be done calculating a torus path integral, but I want to know if an ...
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Why do quasi-free states satisfy the positivity condition?

In LQFT, a state, $\omega$, is a linear map $\omega:A=:CCR({\cal{S}},\Omega)\rightarrow \mathbb{C}$ satisfying: $\omega(aa^{*})\geq 0$ for all $a\in A$. $\omega(I)=1$ where $I$ denotes the identity ...
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Simple, physical explanations for Hadamard behaviour of two-point functions

The two-point function of local quantum fields on a curved spacetime exhibits a singularity of a very particular form, known as Hadamard form, for null separated points $(x,y)$ (including the ...
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Interaction terms in the curved space Lagrangian

Apologies in advance if this has been posted before, I've browsed through the questions but couldn't find anything similar. I've been studying some QFT in curved space (mainly using the Birdell & ...
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Norm definition for arbitrary spin fields in AdS

In AdS/CFT one usually hears of normalizable and non-normalizable modes regarding the independent solutions for the different fields. I've found that the "natural" definition of the norm in the case ...
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Can the fact that the vacuum energy in curved spacetime is not boost invariant be explained without mathematics?

I read in an answer to a question if Hawking radiation can be explained without too much mathematics that this is impossible insofar the vacuum energy is not boost invariant in a curved spacetime. ...
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An explanation of Hawking Radiation

Could someone please provide an explanation for the origin of Hawking Radiation? (Ideally someone who I have been speaking with on the h-bar) Any advanced maths beyond basic calculus will most ...
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What do we know about the semi-classical equation $G_{ab}=\langle T_{ab}\rangle_{\omega}$?

The semi-classical approximation $G_{ab}=\langle T_{ab}\rangle_{\omega}$ is the approximation to the theory of quantum gravity in which one treats matter fields as being quantum in a state $\omega$ ...
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Is there an established theory on statistical physics in curved spacetime?

I tried to check this in google scholar but didn't find a paper explicitly focused on this topic. Do anyone know of some references on this issue? I do not mean the thermodynamics in curved spacetime ...
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Quantum Gravity vs. Quantum Field Theory in Curved Space-time [closed]

I'm a freshman on Physics course, espite of this fact I have a quite interest on Gravitation. My question is: What is the difference between Quantum Gravity and QFT in curved space-time? The great ...
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Imaginary part of the stress-energy tensor

I just encountered in an article of D. G. Boulware ("Quantum Field Theory in Schwarzschild and Rindler Spaces", Phys. Rev. D 11, 1404, 1975, in the last paragraph of the Introduction) the statement ...
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Particle creation through a time dependent Hamiltonian

We know that a time dependent Hamiltonian can create particles. We know this for instance from field theory in curved spacetime, where for instance in an expanding or contracting universe creation and ...
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180 views

Quantization on Minkowski/Schwarzschild spacetimes based on unusual surface

I'm reading the book of Wald "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics", and I'm pondering on this problem: In Minkowski spacetime, we usually quantize our fields with ...
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Merger of old black holes

On the eve of a possible announcement on the production of gravitational waves via a black hole merger, I think this question is quite aptly timed. I have a few questions regarding the evolution of ...
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I need Resources on CMB Neutrinos

I am doing a research paper for upper level undergrad class on CMB neutrinos (C$\nu$B). I need papers that explain CMB Neutrinos from the ground up like the main theory behind the CMB Neutrinos and ...
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How should the path integral change under a dilation?

Let's say I have a two-point function of a scalar field in flat space: $$ \langle \phi(x)\phi(y)\rangle = \int \mathcal D \phi \, \phi(x)\phi(y)\,e^{iS[\phi]} $$ Then I dilate things: $$ \langle \...
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Some questions about curved spacetime QFT

I'm reading Winitzki's Introduction to Quantum Effects in Gravity and I get some questions: In the remark of section 8.3, Page 105. When we calculate the energy-momentum tensor in Rindler space, ...
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Is there any device/technology based on QFT in curved space?

General relativity has given us the GPS, and QFT has provided a big amount of useful technology, from medical treatments to advances in condensed matter. Can QFT in curved space lead to similar ...
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How can we speak use the notion of “particle” in LHC, given that we live in a curved spacetime?

I understood from lectures that the metric of a spacetime was absolute: It does not depend upon the test charge we put inside. Indeed, all the calculation our professor carried out were independent of ...
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Isn't is far more likely that general relativity, and not QFT, is “wrong?” [duplicate]

At the risk/certainty of both sounding super ignorant and talking out of my arse, I have always wondered why there is some big mystery about why there are contradictions between the predictions ...
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Would the detection of advanced waves be possible in curved space-time?

In the transactional interpretation of quantum mechanics reference 1, inspired by the Wheeler–Feynman absorber theory, a transaction is formed between the emitter and absorber by a superposition of ...
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Derivation of Dirac equation in curved spacetime

In all the Literature I have read, the covariant Dirac equation in curved spacetime is given as \begin{equation} \left(i\hbar\gamma^{\mu}(x)\left[\frac{\partial}{{\partial}x^{\mu}}-{\Gamma}_{\mu}(x)...
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Four-momentum and Dirac equation in curved spacetime

Norm of four momentum in Minkowski spacetime is proportional to the square of rest mass as \begin{equation}|P|^2= P^\alpha \eta_{\alpha\beta}P^\beta= (E/c)^2 - p^2 = (mc)^2 \end{equation} While in ...
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Massless limit to massive scalar in AdS space

I was trying to solve massive scalar wave equation in AdS spacetime (or rather in BTZ). I noticed few funny things : The $m\to 0$ limit to the solution is subtle. One of the two independent ...
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Do contractions with Dirac matrices involve a metric?

When figuring out where the spacetime metric enters an equation it is often useful to write all vector indices as covariant indices and write out the inverse metrics that are needed to contract them, ...
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Is Hawking radiation valid for a microscopic black hole?

A black hole evaporates by Hawking radiation. The computation of the evaporation time uses some approximations. Question: Is the evaporation time valid for a microscopic black hole? In particular, ...
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Chronology protection for non-geodesic CTCs and imprisoned curves

As far as I can make out, the quantum part of the Chronology Protection Conjecture hinges on the fact that in curved space, in the semiclassical approximation, the stress energy tensor contains a term ...
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Do quantum wave functions curve spacetime before they are measured

Do wave functions cause spacetime curvature before they are measured, or would curvature only happen upon measurement? I guess the question becomes, do quantum wavefunctions carry energy while they ...
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Assumptions needed to derive Hawking radiation

To derive many singularity theorems in GR you need only assume that GR is correct and the weak energy condition or something similar. My question is what are the assumptions needed to derive Hawking ...
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The classification of particles or fields in general spacetime- Is it still meaningful to say spin-0, 1/2 ,1 field in general spacetime? [closed]

In 3+1 dim Minkovski spacetime, the classification of particle or field, that is spin-0, 1/2 , 1..., depends on the representation of the universal covering group of $SO(1,3)$, that is $SL(2,C)$. When ...
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Are black holes eternal?

The question might sound very easy - Hawking radiation, however I was pondering that as you get closer and closer to a black hole, time dilates exponentially where the surface of the black hole is "...
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How does one correctly interpret the behavior of the heat capacity of a charged black hole?

Note: Although I have a provided an "answer" to the question, I did not resolve all the questions in this post satisfactorily. I invite anyone willing and able to provide a better answer, which I ...
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Wave equation on Schwarzschild background

I am trying to follow the solution of the wave equation for a scalar field on Schwarzschild background from http://batteringram.org/science/gr/scalar_wave.pdf. I have a problem on page 2 where they ...
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Textbook on QFT in curved space-time via path integrals

I am looking for an introductory textbook on QFT in curved space-time via the path integral method. I want to understand the following: How to build a generic perturbative QFT in curved space-time ...
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General relativity and quantum fields evolution in curved space [closed]

There are many cases when we have to discuss the problem of evolution of quantum fields on GR background (inflaton evolution during inflation, axion field evolution etc). But GR isn't quantized as ...
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Nonsingularity of the Euclidean black hole metric

How can one show that the nonsingularity of the Euclidean black hole metric is required for thermal equilibrium of the original black hole in Lorentzian signature? It is mentioned in Prof. P. K. ...
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Is there a natural (suitable) definition for functional derivative in Curved space time

If $$\delta S = \int \sqrt g F[\phi] \delta \phi\tag{1}$$ Then is it natural to define the functional derivative as follows, $$\frac{\delta S}{\delta \phi} = F[\phi].\tag{2}$$ In particular does ...
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Help for project on the basics of the Higgs field

I have a project for my university class on the Higgs fields and how it impacts the standard model. Also I was going to add some information on how the Higgs particle is formed and decays into ...
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Poisson brackets in curved spacetime

The time evolution of any field $\phi$ is given in terms of the Poisson bracket with the Hamiltonian, $$ \frac{\partial\phi}{\partial t} = \{\phi, H\}. $$ How does this relation change in curved ...
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a glaring deficiency in the QFT lagrangian formalism

Summary: In a quantum field theory there is no way to fully constrain the motion of a test-particle using either the equations of motion, or the Noether current, in the presence of gravity. This is ...
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Pass to globally conserved currents from locally conserved currents in curved spacetime

Let us begin with a Lagrangian of the form $$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$ where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
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Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ (\mathcal{A}^{0},\mathcal{A}^{1},\...
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Simplifying effect of a hidden Weyl symmetry in a QFT on curved spacetime

We consider AdS$_{d+1}$ in Poincaré coordinates: $$ ds^2=\frac{1}{z^2}\left(-dt^2+dz^2+dx_{d-1}^2\right), $$ where we set the AdS radius to unity. We study a scalar in this background with action $$ S=...
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Covariant formulation of physical equations?

Is it possible to rewrite equations like the Klein-Gordon, the Dirac or the Proca equation in a generally covariant way? And if yes, how and how can the general covariance be shown? (I searched for ...
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Is there a 2D manifold on which the Dirac equation has a zero mode?

The two-dimensional (2D) Dirac equation $(\sigma_1iD_1+\sigma_2 iD_2)\psi=E\psi$ admits zero mode ($E=0$) solutions on a non-trivial gauge background, such as the zero mode at the core of a U(1) gauge ...
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Gravitational wave contribution of the Hawking radiation from a black hole

Black holes are expected to radiate like a perfect black radiator at the Hawking temperature, which means that they'll emit all particles according to the relevant formulas one can derive using ...
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Eternal black holes and Hawking radiation

I have a fairly simple question which is confusing me a lot. As Hawking showed, a black hole originated by collapse will emit Hawking radiation. This process will reduce the mass of the black hole ...
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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( -\frac{...
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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 ...