Quantum Theory in Curved Spacetime

[alphanzo]

I recently checked out Davies' and Birrell's book "Quantum fields in curved space" and I noticed that it was written in 1982. My question is, did the authors know about the anomalies and that QFT could not incorporate gravity at that time? The table of contents has nothing on anomalies. I am asking because I don't want to read the book only to get to the end and see they were naive.

So another way to pose my question: is the book worth reading, or is there a more modern and accurate perspective modulo string theory?

 

[George Jones]

Birrell and Davis is not about quantum gravity, it is about quantum fields propagating in classical curved spacetime backgrounds. This leads to stuff like the Unruh effect, Hawking radiation, and particle production in expanding universes.

Wald's https://www.amazon.com/dp/0226870278/?tag=pfamazon01-20 is somewhat more recent (1994).

Even more recent is https://www.amazon.com/dp/0521868343/?tag=pfamazon01-20, by Mukhanov and Winitzki (2007). This book is substantially more elementary than the other two books (e.g., only 1+1 spacetime is considered), but, because of this, it can be read in a relatively short period of time.

 

[alphanzo]

thanks, I actually looked at Wald's book but found the equation editor he used unbearably cryptic. My library doesn't have the "Intro..." book so I'll have to look for it elsewhere. I realize that this isn't quantum gravity, however, the equations require one to introduce a curved space metric, implying a graviton, no? Can you self consistently curve the space without having a full curved space theory?

 

[nrqed]

thanks, I actually looked at Wald's book but found the equation editor he used unbearably cryptic. My library doesn't have the "Intro..." book so I'll have to look for it elsewhere. I realize that this isn't quantum gravity, however, the equations require one to introduce a curved space metric, implying a graviton, no? Can you self consistently curve the space without having a full curved space theory?

It's a semiclassical approximation: you quantize the fields while treating the background spacetime classical. So it is an approximation. The question of whether it is self-consistent and in what approximation is it valid is a good one and I will let more knowledgeable people like Georges address this.

By the way the Mukhanov et al book is indeed a gentle introduction and as a bonus there are 40 pages of detailed solutions of the problems given throughout the chapters. It is a bit expensive given that it is relatively short (it's a hardback) but a very valuable reference.

 

[George Jones]

My question is, did the authors know about the anomalies and that QFT could not incorporate gravity at that time?

Which anomalies? The anomalies in string theory and superstring theory whose cancellation requires spacetime to have dimension 26 or 10?

The only connection between these books and sting theory is that if string theory gives a correct theory of quantum gravity, then string theory should (probably), in some appropriate limit, produce the results in these books.

I realize that this isn't quantum gravity, however, the equations require one to introduce a curved space metric, implying a graviton, no?

No gravitons in these books; see nrqed's comments.

Can you self consistently curve the space without having a full curved space theory?

I'm not sure what you mean. Many physicists think that many of the semiclassical results in these books are valid, but I don't think we''ll really know until we have a quantum theory of gravity that fully reproduces these results. This is why I said "probably" above.

So another way to pose my question: is the book worth reading, or is there a more modern and accurate perspective modulo string theory?

This is a very difficult question to answer. What is appropriate and interesting reading very much depends on the person.

If you're interested in the details of the Unruh effect, Hawking radiation, or black hole entropy, then I think you should read some of the stuff in the books already mentioned.

There have been suggestive results in string theory along these lines, but theses results are somewhat exotic.

If you are interested in string theory, maybe you should look at https://www.amazon.com/dp/0521831431/?tag=pfamazon01-20 by Becker, Becker, and Schwarz. 16 String thermodynamics and black holes, is a chapter in the first book, and, 11 Black holes in string theory, is a chapter in the second book. The first book is more elementary than the second.

Maybe you should read Mukhanov and Winitzki (should be available by inter-library loan) followed by Zwiebach, but maybe not.

Whatever works for you!

By the way the Mukhanov et al book is indeed a gentle introduction and as a bonus there are 40 pages of detailed solutions of the problems given throughout the chapters. It is a bit expensive given that it is relatively short (it's a hardback) but a very valuable reference.

I wasn't sure that I wanted to get it, but I'm very glad that I did! I hope to study this book closely over the next couple of months.

 

[alphanzo]

thanks everyone for your comments. I've been persuaded to check out Mukhanov's book. I guess my original question has been answered so I will just make a few comments for clarity.

Which anomalies? The anomalies in string theory and superstring theory whose cancellation requires spacetime to have dimension 26 or 10?

I think so. Specifically the anomalies that arise when one tries to incorporate a curved space connection into the gauge theory and renders the theory non-unitary.

I'm not sure what you mean. Many physicists think that many of the semiclassical results in these books are valid, but I don't think we''ll really know until we have a quantum theory of gravity that fully reproduces these results.

I guess it was a vague question, or at least a difficult question. "Is the semiclassical approximation valid?" I heard that string theory has reproduced Hawking's equation in the context of AdS/CFT but haven't seen the paper. Does anyone know if these calculations are stringy, or are they semi-classical as well?