Physical Foundations of Cosmology by Viatcheslav Mukhanov

[Figaro]

What are the prerequisites to read this book? In the book he stated that there are no GR and QFT knowledge assumed but some people said that it is not true. Can anyone comment on this book? Thanks.

 

[The Bill]

The way Mukhanov's book is written, you can get a lot out of it if you have a very thorough knowledge of undergraduate physics, but you have to work through the book in order very carefully. I'd say the book's necessary minimum prerequisites include a very thorough grounding in relativistic QM, special relativistic mechanics and the geometry of special relativity, and everything that are prerequisites for those. Basically, if you can flip to any page in Shankar or Sakurai and Spacetime Physics and say "I know this thoroughly." then you'll have a rough but manageable time working through Mukhanov slowly.

If you want to use the book as a reference or jump directly to some chapters, then yes, you'd need to have some familiarity with QFT, gauge theory, and GR first to not be lost.

I'd say that at least a passing familiarity with particle theory and GR would be helpful before reading Mukhanov, yes. Practically speaking, I'd say that GR at the level of Schutz and a semester's worth of QFT would be decent prerequisites. You'll at least want good teaching materials on those topics handy as you work through Mukhanov, since you'll be learning them along the way if you're not skipping topics.

 

[Figaro]

The way Mukhanov's book is written, you can get a lot out of it if you have a very thorough knowledge of undergraduate physics, but you have to work through the book in order very carefully. I'd say the book's necessary minimum prerequisites include a very thorough grounding in relativistic QM, special relativistic mechanics and the geometry of special relativity, and everything that are prerequisites for those. Basically, if you can flip to any page in Shankar or Sakurai and Spacetime Physics and say "I know this thoroughly." then you'll have a rough but manageable time working through Mukhanov slowly.

If you want to use the book as a reference or jump directly to some chapters, then yes, you'd need to have some familiarity with QFT, gauge theory, and GR first to not be lost.

I'd say that at least a passing familiarity with particle theory and GR would be helpful before reading Mukhanov, yes. Practically speaking, I'd say that GR at the level of Schutz and a semester's worth of QFT would be decent prerequisites. You'll at least want good teaching materials on those topics handy as you work through Mukhanov, since you'll be learning them along the way if you're not skipping topics.

I've already taken a course in GR by Zee/ A little self study of Carroll, QM by Sakurai, but I haven't done QFT, sadly. In what chapter in Mukhanov should I be familiar with QFT?

 

[The Bill]

I've already taken a course in GR by Zee/ A little self study of Carroll, QM by Sakurai, but I haven't done QFT, sadly. In what chapter in Mukhanov should I be familiar with QFT?

Pretty much all of chapter 4, and snippets of material here and there after that.

Edit: since you've got Sakurai, make sure you have an excellent understanding of *all* of the material in Sakurai's chapters 5 and 7.

 

[Figaro]

Pretty much all of chapter 4, and snippets of material here and there after that.

Edit: since you've got Sakurai, make sure you have an excellent understanding of *all* of the material in Sakurai's chapters 5 and 7.

Oh, perturbation theory, of course, it's Mukhanov. But how do I tackle chapter 4 if that is the case? Or can I skip it without disrupting the flow? I'm leaning towards inflation so I'd like to focus in that part of Mukhanov.

 

[The Bill]

Oh, perturbation theory, of course, it's Mukhanov. But how do I tackle chapter 4 if that is the case? Or can I skip it without disrupting the flow? I'm leaning towards inflation so I'd like to focus in that part of Mukhanov.

You'll be fine for most of Mukhanov's discussion of inflation. If you want to understand his presentation completely without skipping material and taking things on faith, you'll need some QFT. The QFT you'd want for a full understanding is everything leading up to an understanding of how individual Feynman diagrams coresspond to terms in a field's Lagrangian.

But yeah, if you can take the QFT parts on faith, you can skim them and focus on Mukhanov's descriptions of inflationary models, which mostly depend on GR concepts like the Friedmann equations.

 

[Figaro]

You'll be fine for most of Mukhanov's discussion of inflation. If you want to understand his presentation completely without skipping material and taking things on faith, you'll need some QFT. The QFT you'd want for a full understanding is everything leading up to an understanding of how individual Feynman diagrams coresspond to terms in a field's Lagrangian.

But yeah, if you can take the QFT parts on faith, you can skim them and focus on Mukhanov's descriptions of inflationary models, which mostly depend on GR concepts like the Friedmann equations.

I think I'd be fine if that is the case, thank you very much for your response!

 

[George Jones]

make sure you have an excellent understanding of *all* of the material in Sakurai's chapters 5 and 7.

Which edition of Sakurai? In the the revised first edition, chapters 5, 6, and 7 are "Approximation methods", "Identical Particles", and "Scattering Theory", while the in second edition, the order is changed to "Approximation methods", "Scattering Theory", and "Identical Particles".

The second edition has added a section on quantization of the electromagnetic field (without interactions), and has added a new chapter 8, "Relativistic Quantum Mechanics".

 

[The Bill]

Which edition of Sakurai?

Oops, I forgot to mention I was referring to the 1994 revised edition.

 

[vanhees71]

If "relativistic quantum mechanics" is not relativistic QFT but some old-fashioned handwaving like Dirac's old hole theory, I'd rather take this as a bug than a feature of any textbook on the subject. This "historic" approach to relativistic QT has the disadvantage that you have to almost everything forget to get your mind free for the (nearly) true thing, which is relativistic QFT as used in the Standard Model.

 

[The Bill]

If "relativistic quantum mechanics" is not relativistic QFT but some old-fashioned handwaving like Dirac's old hole theory, I'd rather take this as a bug than a feature of any textbook on the subject.

I wouldn't call what I meant "some old-fashioned handwaving like Dirac's old hole theory," no. To me "relativistic quantum mechanics" is shorthand for "basic but modern coverage of the Dirac equation, perturbation theory, and path integrals for the benefit of students who might go on to study quantum field theory." But, that's a bit of a mouthful, so I just call it "relativistic quantum mechanics." My typical touchstone for it is the last few chapters of Shankar.

 

[vanhees71]

Is it using "first-quantization arguments" and talks about the solutions of the Dirac equation as "wave function" or is it using quantum field theory right from the beginning (as I strongly suggest to teach the subject)?

 

[The Bill]

Is it using "first-quantization arguments" and talks about the solutions of the Dirac equation as "wave function" or is it using quantum field theory right from the beginning (as I strongly suggest to teach the subject)?

Shankar briefly treats the Dirac equation as a wave function, shows the limitations of that approach, and uses it as motivation for why quantum field theory is necessary. The failure you're talking about is used as a pedagogical tool to prod the reader on to QFT, using the tools of a regular quantum mechanics course to motivate the need for the transition. Not many pages are spent in this. It's not extolling the virtues of this and that application of pre-QFT RQM, quite the opposite.

If these books treated full QED the way you suggest, they would be QFT textbooks, not QM textbooks.

 

[vanhees71]

Yes, that's why I think that QM textbooks shouldn't contain relativistic QT at all. Of course, as a motivation for why the "1st quantization" approach doesn't work in the relativistic case, it's very good to discuss it. That's also done in Peskin&Schroeder in the very beginning.

 

[The Bill]

I disagree. Many students want to see the Dirac equation and spinors. Covering this material(with an appropriate note of caution) can give them a taste of what they could accomplish in a QFT class. also, giving them some experience with SU(2) is helpful.

There are reasons not do all things exactly the way they're done "for real" the first time they're taught. We teach Newtonian gravity extensively even though relativistic corrections are used in essentially *all* real life orbital calculations due to the precision of modern timekeeping and radio equipment. And we reap a reward in teaching Newtonian theory as a pedagogical tool.

Three or four hours spent teaching the Dirac equation has benefits you're not acknowledging.