Does a localised particle created with a QFT on curved spacetime follow geodesics?

Question

I was wondering if there is a result, analogous to the Ehrenfest theorem in quantum field theory (QFT), and in particular if the QFT is on a curved spacetime.

In the last case, I would expect to obtain an equation which resembles the geodesic equation, but I am not able to do the calculation and I have searched online but found nothing.

Níckolas Alves · Answer 1 · 2024-03-23T14:44:03.403

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The notion of particle is not well-defined in quantum field theory in curved spacetime (QFTCS). What is a particle will depend on which observer you are considering. In quantum field theory, particles are merely an observer-dependent interpretation. The theory is described in terms of quantum fields.

In ordinary quantum mechanics you have a very different picture in which the wavefunction describes a single particle (even though it is not a localized particle in principle), so you can obtain a "classical particle"-like description.

I wouldn't be surprised if you have a version of Ehrenfest's theorem in that the expectation values of the fields satisfy the classical wave equations or something of the sort (I'm not sure if this does hold), but to recover a notion of classical particles from QFTCS seems extremely unlikely for me (where I'm trying my best to not say impossible).

edited Mar 23 '24 at 14:44

answered Mar 22 '24 at 19:46

Níckolas Alves

17,567

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What is the reason curved spacetime makes the notion of particle not well defined? Is this also true for flat spacetime? – Pato Galmarini Mar 22 '24 at 21:42
What is QFTCS ? – magma Mar 23 '24 at 07:21
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I do not really care for a general result which holds in all coordinate systems. For example I would be rather happy to see that in an asymptotically flat spacetime, for an observer infinitely far away from the gravitational source, a particle wavepacket follow the geodesics. I do not know if there is a scattering formalism that do not use on the S matrix, which hides all the details of the interaction. In this case, i do not want to know just the In and Out states, but what's happening during the interaction. – Sebastiano Tomasi Mar 23 '24 at 14:33
@PatoGalmarini See this answer of mine – Níckolas Alves Mar 23 '24 at 14:46
@magma quantum field theory in curved spacetime (I clarified this in the answer, thank you for pointing it out) – Níckolas Alves Mar 23 '24 at 14:46
@SebastianoTomasi In this case I have no idea about whether the particle modes follow geodesics in some sense or not – Níckolas Alves Mar 23 '24 at 14:47
Thanks!......... – Pato Galmarini Mar 24 '24 at 00:28

Does a localised particle created with a QFT on curved spacetime follow geodesics?

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