# Particle definition in arbitrary spacetimes

1. Aug 17, 2011

### femtofranco

Hello, I am reading up on QFT in curved spacetimes, and am aware that states of QFT's in such spacetimes, have, in general, no physically meaningful particle definitions. I was just hoping someone could clarify what is meant by "physically meaningful."

2. Aug 18, 2011

### Demystifier

It means covariant, or independent on the choice of the time coordinate.
Sometimes it may mean independent on the observer, but others may say that observer dependence is physically meaningful.

3. Aug 18, 2011

### francesca

http://arxiv.org/abs/gr-qc/0409054" [Broken]
What is a particle? by Daniele Colosi and Carlo Rovelli
Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have lead some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators. Still, it is not obvious how to reconcile this view with the empirically-observed ubiquitous particle-like behavior of quantum fields, apparent for instance in experimental high-energy physics, or "particle"-physics. Here we offer an element of clarification by observing that already in flat space there exist --strictly speaking-- two distinct notions of particles: globally defined $n$-particle Fock-states and *local particle states*. The last describe the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance for flat-space theories --it amounts to a reminder that there are boundary effects in realistic detectors--; but is relevant for gravity. It reconciles the two points of view mentioned above. More importantly, it provides a definition of local particle state that remains well-defined even when the conventional global particle states are not defined. This definition plays an important role in quantum gravity.

I found it very helpful, hope you will enjoy it!
Best, Frances

Last edited by a moderator: May 5, 2017
4. Aug 18, 2011

### femtofranco

Thank you, both. The whole matter seems much clearer to me.

And I must say, that was a lovely article.