Book/PDF # Field Theory / Langrangians / Variations

[ProfDawgstein]

Hey,

I am looking for a book / paper / pdf which covers things like

-maxwell EM field theory
-gravitational field theory
-variational calculus / principle of least action
-lagrangian mechanics
-basic scalar fields / wave equations
-field equations out of lagrangians
-maybe some basic quantum field theory

-Symmetries and Noethers Theorem
-Non-relativistic Lagrangian Fields
-Maxwell and GR lagrange (GR + EM field equations)
-string theory / m-theory (optional)

Background:
------------

-mechanics
-basic field theory (lecture videos)
-EM
-calculus of variations (but almost no experience)
-basic general relativity

Examples of things it should contain:
-----------------------------------

Gravity:

$\delta g_{ab}$

$\delta \Gamma^{a}_{bc}$

$\mathcal{L}_G = \sqrt{-g} R$

$S=\frac{1}{16\,\pi}\int \mathrm{d}^4x \sqrt{-g}\left(\phi\, R - \omega\,\phi^{-1}\partial_{\mu}\phi\,\partial^{\mu}\phi\right)+S_\mathrm{M}$

Maxwell EM:

$\delta F_{ab}$

$F_{ab} F^{ab}$

Other fields:

$\partial_\mu \phi \partial^\mu \phi$

$\mathcal{S} = \int \, \mathrm{d}^4 x \sum_{i=1}^n \left[ \frac{1}{2} \partial_\mu \varphi_i \partial^\mu \varphi_i - \frac{1}{2}m^2 \varphi_i^2 \right]$

Requirements:
-------------

-Solutions would be nice (or at least hints)
-quite detailed
-no graduate math textbooks please :)
-physics background
-rigorous
-some worked examples (!)

Thank you in advance.

 

[robphy]

This may be good:
Doughty https://www.amazon.com/dp/0201416255/?tag=pfamazon01-20
www.worldcat.org/title/lagrangian-interaction-an-introduction-to-relativistic-symmetry-in-electrodynamics-and-gravitation/oclc/20798391

 

[ProfDawgstein]

This may be good:
Doughty https://www.amazon.com/dp/0201416255/?tag=pfamazon01-20
www.worldcat.org/title/lagrangian-interaction-an-introduction-to-relativistic-symmetry-in-electrodynamics-and-gravitation/oclc/20798391

This one looks interesting. Thanks!
It's a shame you can't look inside...

A few worked examples would be nice.
But that is definitely a good start!

 

[Daverz]

For mechanics, I like Landau & Lifschitz.

You can find some good basic notes on QFT here:

http://www.damtp.cam.ac.uk/user/tong/qft.html

I'd also recommend Field Quantization in the Greiner series. It does a good job of covering many of the basics.

A recent GR book that emphasizes the action is Zee's nutshell book.

https://www.amazon.com/dp/069114558X/?tag=pfamazon01-20

 

[ProfDawgstein]

For mechanics, I like Landau & Lifschitz.

You can find some good basic notes on QFT here:

http://www.damtp.cam.ac.uk/user/tong/qft.html

I'd also recommend Field Quantization in the Greiner series. It does a good job of covering many of the basics.

A recent GR book that emphasizes the action is Zee's nutshell book.

https://www.amazon.com/dp/069114558X/?tag=pfamazon01-20

Thank you.

Landau & Lifschitz

pretty old and not really good for learning anything?
It seems that nobody likes those books, I have never checked them out myself though.

http://www.damtp.cam.ac.uk/user/tong/qft.html

already have them, they are not bad.
But I wanted to do some "basic" field theory first, QFT will come after GR one day.

Field Quantization

I really liked that book. Didn't understand too much of it though... :D
That one focuses on QM/QFT too much.

Zee's nutshell book

I don't know. The whole book looks like a big mess to me :|
More like a reference than a book to learn from.

[these are just impressions, I haven't worked trough any of them]

My priority at the moment is : Maxwell, GR, GR + various other fields

 

[WannabeNewton]

pretty old and not really good for learning anything?
It seems that nobody likes those books, I have never checked them out myself though.

Nobody likes Landau and Lifshitz? That's got to be the first time I've heard that lol. Just because a book is old doesn't mean it isn't good. These books are considered some of the most elegant in physics. Classical mechanics hasn't needed an update in years upon years upon years.

 

[AnTiFreeze3]

... pretty old and not really good for learning anything?
It seems that nobody likes those books, I have never checked them out myself though ...

Well... no.

http://en.wikipedia.org/wiki/Course_of_Theoretical_Physics

 

[ProfDawgstein]

Nobody likes Landau and Lifshitz? That's got to be the first time I've heard that lol. Just because a book is old doesn't mean it isn't good. These books are considered some of the most elegant in physics. Classical mechanics hasn't needed an update in years upon years upon years.

I heard:
-highly advanced math (written for people who know A LOT OF math)
-you need some background already to understand them

Just because a book is old doesn't mean it isn't good

Do not take that one too serious :)

Classical mechanics hasn't needed an update in years upon years upon years.

That is true.

I am only talking about the 'mechanics' edition.

 

[micromass]

I heard:
-highly advanced math (written for people who know A LOT OF math)
-you need some background already to understand them

That doesn't mean that nobody like them. Quite the contrary.

 

[ProfDawgstein]

That doesn't mean that nobody like them. Quite the contrary.

Ok. Maybe I was a bit too harsh...

From the perspective of 'self study' they are pretty bad.
I only remember negative reviews from people saying that it's a bad idea trying to learn
mechanics from that book.
Somebody also said you need to be quite a genius to understand them.

Just telling you what I know about them.
This might not be true, so feel free to convince me that it's a good book.

 

[Daverz]

I heard:
-highly advanced math (written for people who know A LOT OF math)

I wouldn't say so.

-you need some background already to understand them

L&L's Mechanics is not an intro mechanics book, but you should be fine if you know undergrad mechanics (e.g. at the level of Fowles, Analytical Mechanics).

There's always Goldstein if you want a tome.

 

[ProfDawgstein]

I wouldn't say so.

L&L's Mechanics is not an intro mechanics book, but you should be fine if you know undergrad mechanics (e.g. at the level of Fowles, Analytical Mechanics).

There's always Goldstein if you want a tome.

Well, I guess I listened to the wrong people then...

This https://www.physicsforums.com/showthread.php?t=666566 made me think even less of their
mechanics book...

Is it true that the new books are better than the old ones, didactically?
(This is probably the reason why I want a newer book)

I have "Electrodynamics and Classical Theory of Fields and Particles (A. O. Barut)", which is
quite good. But no GR...

 

[Daverz]

I really liked that book. Didn't understand too much of it though... :D
That one focuses on QM/QFT too much.

The first 2 chapters may still be useful review for your program.

I don't know. The whole book looks like a big mess to me :|
More like a reference than a book to learn from.

It may be true that because I'm more familiar with GR that Zee's "Gravity" book seems much more readable to me than his QFT book.

I mention it because of the formula for the GR action in your original post. Zee emphasizes the action more than any other book I've seen at that level. He also covers Feynman's field theoretic approach.

You might also like the approach in Ohanian:

https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

My priority at the moment is : Maxwell, GR, GR + various other fields

This recent book may be of interest:

https://www.amazon.com/dp/3642279848/?tag=pfamazon01-20

There's also the little -- and, oh dear, very old -- book by Barut:

https://www.amazon.com/dp/0486640388/?tag=pfamazon01-20

My favorite EM book is Schwartz, Principles of Electrodynamics, but he doesn't cover variational methods at all.

 

[ProfDawgstein]

You might also like the approach in Ohanian:

https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

That part looks really good, but I want a lot more.

Basically a whole book filled with that sort of stuff, doing all kinds of variations/actions.

https://www.amazon.com/dp/0486640388/?tag=pfamazon01-20

Just edited this one in, see my last post.

This recent book may be of interest:

https://www.amazon.com/dp/3642279848/?tag=pfamazon01-20

It also has solutions, nice.

Thanks a lot.

 

[Daverz]

Well, I guess I listened to the wrong people then...

This https://www.physicsforums.com/showthread.php?t=666566 made me think even less of their
mechanics book...

To be honest, of the books in the series that I have, Mechanics is the only one I've used much.

Is it true that the new books are better than the old ones, didactically?

Not as a general rule.

 

[WannabeNewton]

So are you basically just looking for a book on classical field theory?

 

[ProfDawgstein]

So are you basically just looking for a book on classical field theory?

if that contains GR, EM, Scalar fields, basic QFT fields. Yes, kind of.

 

[ProfDawgstein]

It may be true that because I'm more familiar with GR that Zee's "Gravity" book seems much more readable to me than his QFT book.

I also find the whole layout confusing.

He moves a lot of stuff into the appendices in the end of the chapter,
but there are also appendices at the end of the book.

Some of the things from the appendices should have been covered in the main chapter.
I really don't know why he did that...

 

[Daverz]

Couple of other books that should be mentioned:

http://insti.physics.sunysb.edu/~siegel/Fields3.pdf

Not originally mentioned because I don't like his writing (OK, I don't understand his writing ;) ). YMMV.

And the old book by Soper:

https://www.amazon.com/dp/0486462609/?tag=pfamazon01-20

I have a short review of the previously mentioned Doughty book on Amazon:

 

[George Jones]

By "basic QFT fields", do you mean basic quantum theory of free scalar fields? Free EM fields? Interacting fields, including regularization and renormalization?

 

[ProfDawgstein]

By "basic QFT fields", do you mean basic quantum theory of free scalar fields? Free EM fields? Interacting fields, including regularization and renormalization?

scalar fields, dirac, klein gordon, qed without 'regularization and renormalization'.

Mostly lagrangians and field equations.

'how to construct langrangians' (symmetries, invariance, ...) would be also interesting.

 

[George Jones]

Then maybe the first volume of Aitchison and Hey has both more and less than you want,

https://www.amazon.com/dp/1466512997/?tag=pfamazon01-20

 

[ProfDawgstein]

Then maybe the first volume of Aitchison and Hey has both more and less than you want,

https://www.amazon.com/dp/1466512997/?tag=pfamazon01-20

Bookmarked. Will check out when it's time :)
Thank you anyway.

 

[bolbteppa]

Your question is almost perfectly answered (bar string theory) in a mixing of Gelfand's Calculus of Variations book along with Landau volume 2, & you could use Kiselev-Krasnov's Problems & Exercises in the Calculus of Variations for exercises with answers to go along with Gelfand. The combination of these three is hours & hours & hours of poetry, the only better thing than this would be a problem book to go along with Landau in detail (hint hint ), and this guy

http://gr-lectures-paddy.blogspot.ie/

gives great intuition for most of volume 2! Landau is quite literally the best thing I've ever read & will continue to read for the next two years, at least...

 

[WannabeNewton]

Speaking of which, Padmanabhan's GR text is also something you can look into. The entirety of chapter 2 is devoted to classical fields, mainly the EM field. Later chapters include the Hamiltonian formulation of GR, which imo is more complicated than the Lagrangian formulation.

 

[dextercioby]

The Greiner series (a German version of the Russian L-L) contains at least 2 volumes on Field Theory: Relativistic Wave Equations and Field Quantization.

 

[ProfDawgstein]

Your question is almost perfectly answered (bar string theory) in a mixing of Gelfand's Calculus of Variations book along with Landau volume 2, & you could use Kiselev-Krasnov's Problems & Exercises in the Calculus of Variations for exercises with answers to go along with Gelfand. The combination of these three is hours & hours & hours of poetry, the only better thing than this would be a problem book to go along with Landau in detail (hint hint ), and this guy

http://gr-lectures-paddy.blogspot.ie/

gives great intuition for most of volume 2! Landau is quite literally the best thing I've ever read & will continue to read for the next two years, at least...

Nice, finally some lectures which have good quality.
I will definitely check out Landau 2.

Also have this one "Calculus of Variations (Dover Books on Mathematics) [Robert Weinstock]".

Padmanabhan's GR

100% going to do that :)

Field Theory: Relativistic Wave Equations and Field Quantization

'Field Quantization' looked really good (did not read it).

Thank you all.

Now I just need a 48hour-day (:P)

 

[ProfDawgstein]

You might also like the approach in Ohanian:

https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

I just did a few pages of the appendix (variational principle and energy momentum tensor) and it's awesome! Thank you for the hint :)
I probably wouldn't have touched that book for a few weeks, nor had looked into the appendix...

 

[Daverz]

Another book I'd forgotten:

https://www.amazon.com/dp/0486438171/?tag=pfamazon01-20