Classical New E&M Text by Wald - Princeton Press 30% Off

[MidgetDwarf]

[Mentor Note -- this thread about Wald's text split off from this thread start about book discounts:]

https://www.physicsforums.com/threads/princeton-press-30-till-july-31-2022.1010897/

 

[Frabjous]

I am looking at the physics catalogue and a 30% code through 15 March is on the web page.

Apparently Wald is coming out with an E&M text in March. I really want to read the first chapter.

• CHAPTER 1 Introduction: Electromagnetic Theory without Myths
  • 1.1 The Fundamental Electromagnetic Variables Are the Potentials, Not the Field Strengths
  • 1.2 Electromagnetic Energy, Momentum, and Stress Are an Integral Part of the Theory
  • 1.3 Electromagnetic Fields Should Not Be Viewed as Being Produced by Charged Matter
  • 1.4 At a Fundamental Level, Classical Charged Matter Must Be Viewed as Continuous Rather Than Point-Like

 

[vanhees71]

If it were not Wald, I'd expect some crackpotery ;-)).

 

[Keith_McClary]

I really want to read the first chapter.

• CHAPTER 1 Introduction: Electromagnetic Theory without Myths

Here (with one page missing ).

 

[Demystifier]

1.1 The Fundamental Electromagnetic Variables Are the Potentials, Not the Field Strengths

I often say that too, but people usually don't get it. Now when Wald says that, I hope people will finally start to pay attention.

 

[ergospherical]

Apparently Wald is coming out with an E&M text in March.

May I ask what is novel about this textbook, or in other words, it's "raison d'être"? The contents list and the material in the Google books preview looks like the standard electromagnetism theory covered already quite extensively in many existing books. (But then again, it is Wald, so I would not like to judge it so soon!).

 

[dextercioby]

He argues against the thesis: „charges are not the sources of the electromagnetic fields”. I would say, OK. Then we would be expecting some electromagnetic field surrounding chargeless matter (a hypothetical lump of Higgs bosons). How did the field get there in the first place?

 

[Demystifier]

He argues against the thesis: „charges are not the sources of the electromagnetic fields”. I would say, OK. Then we would be expecting some electromagnetic field surrounding chargeless matter (a hypothetical lump of Higgs bosons). How did the field get there in the first place?

If we take the usual view that charges are the source of EM fields, then you have an analogous question: How did the charges get there in the first place?

Questions of that kind are a matter of initial conditions, physics does not have answers to such questions. The point is that Maxwell equations with zero sources have nontrivial solutions, so in theory EM fields can exist without charges.

 

[vanhees71]

I often say that too, but people usually don't get it. Now when Wald says that, I hope people will finally start to pay attention.

Well, let's wait what Wald writes. I'm very skeptical. What's physically significant are observables, and observables are gauge invariant. In quantum field theory (retarded) correlation functions of gauge-invariant local observables are the mathematical expressions which describe observable quantities. That also includes the observables related to the Aharonov-Bohm effect(s).

 

[Demystifier]

Well, let's wait what Wald writes.

You don't need to wait. This section can already be seen in the link in #4.

What's physically significant are observables, and observables are gauge invariant. ... That also includes the observables related to the Aharonov-Bohm effect(s).

But as you know, the Aharonov-Bohm gauge-invariant observable is expressed in terms of the potential, not in terms of the magnetic field, provided that you insist on a local description. It all boils down to the fact that the integral $\int dx^{\mu}A_{\mu}$ is gauge invariant, so it's not really necessary to deal with $F_{\mu\nu}$ in order to have a gauge-invariant quantity.

 

[vanhees71]

Yes, it's the gauge-invariant non-integrable phase factor $\exp(\mathrm{i} \int \mathrm{d} \vec{r} \cdot \vec{A})$ that is observable here but not the potential itself. I'm pretty sure that Wald doesn't do anything wrong, but the quoted section titles are at least provocative ;-)).

 

[Demystifier]

Note also that you must vary action over $A_{\mu}$, not over $F_{\mu\nu}$, to obtain the equations of motion from the action. Similarly, in path-integral quantization, you must integrate over $A_{\mu}$, not over $F_{\mu\nu}$. Likewise, in canonical quantization, ... well, I'm sure you know. All that points to the conclusion that the fundamental (which is not the same as observable) theoretical quantity is $A_{\mu}$, not $F_{\mu\nu}$.

Furthermore, if one insisted that "fundamental" should mean "observable", then what would be a "fundamental" thing for the Dirac field? I believe the Dirac field illustrates very well the idea that "fundamental" and "observable" must be thought of as different concepts.

 

[vanhees71]

No! It's $A_{\mu}$ modulo gauge transformations. Without this important qualification you cannot "canonically quantize" gauge theories to begin with!

It's a priori clear for the Dirac field as a fermionic field that the observables must be built from correlation functions of even rank. For the free field the 16 invariant forms $\bar{\psi}(x) \Gamma \psi(x)$ are the local observables. The field itself doesn't represent local observables since it doesn't fulfill the microcausality condition due to the fermionic instead of bosonic commutation relations.

 

[dextercioby]

If we take the usual view that charges are the source of EM fields, then you have an analogous question: How did the charges get there in the first place?

Questions of that kind are a matter of initial conditions, physics does not have answers to such questions. The point is that Maxwell equations with zero sources have nontrivial solutions, so in theory EM fields can exist without charges.

OK, I am buying this explanation. Thank you!

 

[Demystifier]

No! It's $A_{\mu}$ modulo gauge transformations. Without this important qualification you cannot "canonically quantize" gauge theories to begin with!

Right, but $A_{\mu}$ modulo gauge transformations is not the same as $F_{\mu\nu}$. So the point is that the fundamental quantity is $A_{\mu}$ modulo gauge transformations, not $F_{\mu\nu}$.

$\bar{\psi}(x) \Gamma \psi(x)$ are the local observables.

Exactly! But still, the fundamental quantity is $\psi$, not $\bar{\psi} \Gamma \psi$.

 

[vanhees71]

That's a bit about semantics. In a sense the Dirac field are fundamental mathematical building blocks, because they provide a local realization of an irrep of the orthrochronous (not the proper orthochronous, for which the two possible Weyl spinors are the irreps with spin 1/2) Poincare group.

 

[hutchphd]

May I ask what is novel about this textbook, or in other words, it's "raison d'être"?

Trivially I would point to preface where the author gives his reason.
I thought section 1.4 was pretty interesting at first read. This looks like an interesting contrast in style to Jackson as standard graduate text. We shall see.

 

[robphy]

I really want to read the first chapter.

Here (with one page missing ).

I can see the entire first chapter in Amazon's preview
https://www.amazon.com/dp/0691220395/?tag=pfamazon01-20
and on the Princeton site
https://press.princeton.edu/books/h...0/advanced-classical-electromagnetism#preview

You can also read the preface on the Amazon site.

Some hightlights:

This book arose from my teaching the first quarter of the standard graduate course in electromagnetism at the University of Chicago in the winter of 2018.

...rethink how the subject of electromagnetism should
be presented at the graduate level. When I did so, it became dear to me that the usual
quasi-historical way of presenting the subject promotes some very unhealthy ways of
thinking about electromagnetism. Therefore, to avoid starting off on the wrong foot,
I decided to spend the first few lectures of the course describing what I now refer to in
chapter 1 of this book as "myths" concerning electromagnetism. I found that by starting
out in this way, it became much easier to straightforwardly present the subject in a
clear and concise manner, without having to make shifts in perspective as the subject is
developed.

...
The topics treated in chapters 2-7 are ones that normally would be covered in any
graduate course in electromagnetism. Electrostatics is treated in chapter 2, but starting with Poisson's equation, not Coulomb's law.

...
Special relativity is discussed in chapter 8. ...
I have put considerable care into writing section 8.1 in such a way that it introduces special relativity in a conceptually clear way without introducing more abstraction than I believe to be essential.
...
Chapter 9 discusses electromagnetism as a gauge theory, thereby bringing the formulation of electromagnetism in this book up to the level of conceptual understanding that
was achieved by the mid-twentieth century.
...
Finally, the notion of a point charge is discussed in depth in chapter 10. lt is shown that a mathematically well-defined limit of a charged body as it shrinks down to zero size can be taken provided that one also takes the charge and mass of the body to scale to zero proportionally to its size. Lorentz force motion is in this limit. ...

One quarter at the U of C is about 10 weeks.
So, this is a short book (less than 250 pages).
The book appears not to be a replacement for (say) Jackson in terms of scope or detail.

Of interest:
Robert Wald: Point Particles and Self-Force in Electromagnetism
Start at t=6m20.

 

[vanhees71]

It's not downloadable as pdf. That's too hard to read...

 

[hutchphd]

I note that with the code PUP30 at the Princeton U Press the hardcover cost is $35...! I've ordered one (March 22 2022 )

 

[vanhees71]

The paper on the radiation-reaction problem mentioned in the youtube-movie is here:

https://arxiv.org/abs/0905.2391v2

 

[robphy]

The paper on the radiation-reaction problem mentioned in the youtube-movie is here:

https://arxiv.org/abs/0905.2391v2

Here are Wald's slides on the "rigorous derivation of the Self-force"
http://www2.yukawa.kyoto-u.ac.jp/~soichiro.isoyama/CAPRA/CAPRA_2009/09_Wald2.pdf

Here are Wald’s slides on a less-technical discussion of the "Self-Force"
https://web.math.utk.edu//~fernando/barrett/bwald1.pdf
The last few slides may also be of interest.
Here is a related talk at Perimeter.
https://pirsa.org/10040030

Here is the gravitational version of the paper referenced by @vanhees71 :
A Rigorous Derivation of Gravitational Self-force
Samuel E. Gralla, Robert M. Wald
https://arxiv.org/abs/0806.3293
and related slides
http://www2.yukawa.kyoto-u.ac.jp/~soichiro.isoyama/CAPRA/CAPRA_2008/08_Wald.pdf

 

[martinbn]

I often say that too, but people usually don't get it. Now when Wald says that, I hope people will finally start to pay attention.

Not to derail the thead, but I think that you and he have a different view on this although you both say it.

 

[Demystifier]

Not to derail the thead, but I think that you and he have a different view on this although you both say it.

What's the difference?

 

[martinbn]

What's the difference?

The way I understand him and you, you might disagree, is that he has a very clear view on the metaphysics. For him the electromagnetic field has ontology on equal footing with the other types of matter say electrons. This much he says. The $E$ and $B$ and the $A$ and $\varphi$ on the other hand are part of the mathematical discription. The second pair is more fundamental, but that is question of the mathematics not metaphysis. For you, the way I understand your view, the $E$ and $B$ and the $A$ and $\varphi$ can have ontology, which leads to a very confused notion of what exists and what is real.

 

[Demystifier]

The way I understand him and you, you might disagree, is that he has a very clear view on the metaphysics. For him the electromagnetic field has ontology on equal footing with the other types of matter say electrons. This much he says. The $E$ and $B$ and the $A$ and $\varphi$ on the other hand are part of the mathematical discription. The second pair is more fundamental, but that is question of the mathematics not metaphysis. For you, the way I understand your view, the $E$ and $B$ and the $A$ and $\varphi$ can have ontology, which leads to a very confused notion of what exists and what is real.

If you look at my arguments in this thread, you will see that I don't refer to ontology and reality.

 

[martinbn]

If you look at my arguments in this thread, you will see that I don't refer to ontology and reality.

Yes, but this

I often say that too, but people usually don't get it. Now when Wald says that, I hope people will finally start to pay attention.

means other threads where you have expressed your view as well. But if I have misunderstood you then you can correct me.

 

[Demystifier]

Yes, but this

means other threads where you have expressed your view as well. But if I have misunderstood you then you can correct me.

Well, sometimes I say that in the context of ontology, but that's not the only context where I say that.

 

[martinbn]

Well, sometimes I say that in the context of ontology, but that's not the only context where I say that.

So do you have the same view as him the way I wrote it here

For him the electromagnetic field has ontology on equal footing with the other types of matter say electrons. This much he says. The $E$ and $B$ and the $A$ and $\varphi$ on the other hand are part of the mathematical discription. The second pair is more fundamental, but that is question of the mathematics not metaphysis.

 

[Demystifier]

So do you have the same view as him the way I wrote it here

I agree, at least in the context of classical physics.