The Classical Theory of Fields: Volume 2

Landau's approach to Classical Field Theory demonstrates his ability to be clear, concise, and elegant without drowning out the physics with math. I will say, however, that Landau requires a certain maturity to appreciate his style (same goes for Rudin's books of analysis). I would recommend this title to those with a working knowledge of classical E & M, vector/tensor analysis, and of special relativity. It is also wise to work through the author's Theoretical Mechanics to get a taste of their style. I believe, contrary to many, that this book is appropriate for self study if one is willing to do the work (not only the exercises but following along pencil in hand). I suggest reading a passage and then covering it up and then trying to do the derivations by hand. My only complaint is the quality of print, which has is not the fault of the authors. It is especially annoying at first.

The author builds up a whole theory from almost nothing but common sense. You soon find yourself on page 150 as if you are reading Jane Austin. Landau's exposition is detailed but not boring, he gets to the fundamental facts right away. They define the electromagnetic field as derivatives of a potential. Great insight for people with background in mathematics. I always heard 'The electromagnetic field is the curvature of the connection.' but I didn't quite understand what they meant by that. Now I know.

In depth description of classical field theory by landau and lifschitz.

Landau was a master: Concise, insightful, and capable of prodding the student's intellect to solve problems for oneself.As this text elucidates, Electrodynamics cannot be properly understood without the uber-principle of Relativity as foundation; and that is just the beginning.I am still fascinated and a little exhilarated every time I am reminded of the Gauge Invariance associated with the Electrodynamic field. Landau broaches this subject near the very beginning of the text (Paragraph 18) in an elegant way. Because the definitions of the Magnetic field (B) and Electric field (E) contain only the DERIVATIVES of the corresponding potentials rather than the potentials themselves (A, and phi, respectively), it's easily proven that adding constants to the potentials will not affect the field intensities (remember the derivative of a constant = zero!).Here's the MathExample: E Field only:E = -1/c (dA/dt) - grad(phi)But if we change A and phi by adding constants to them, i.e.:A' = A + grad(f)phi' = phi - 1/c(df/dt)Thus, the new field E' = -1/c (dA'/dt) - grad (phi')or, expanding:E' = -1/c (dA/dt) - 1/c (d/dt grad(f)) - grad (phi) + 1/c grad (df/dt)The second and fourth terms on the right cancel, so E' = -1/c (dA/dt) - grad (phi) = E.The field intensity is unchanged despite changing the potentials.Same result obtains when considering the Magnetic field B = curl AAnother bombshell is that no matter how one is moving, the total Electrodynamic field does not change. Relative motion will change the measured intensity of the magnetic component B, or perhaps the electric component E depending on how one is moving, but there will always be a resultant compensating change in the one component when there is a change in the other, such that the full field remains unchanged. This represents the essential truth that the Electrodynamic field is a TENSOR, whose physical character is not affected by relative motion; it is invariant in any reference frame.Consider the profound ramifications bound in that concept: A light wave whose existence begins on the surface of some star, potentially traverses 6 or 7 reference frames before it is absorbed in some planets' atmosphere, or perhaps within a leaf. If a measurement is performed on that light wave within any of those reference frames, that measurement will betray the character of said reference frame; so in a sense, perhaps the electromagnetic (electrodynamic!) wave serves as a UNIVERSAL FRAME OF REFERENCE: TRULY INERTIAL.Mirror image of that statement is that if one could rather travel with the wave, as Einstein envisioned, one would "see" the rest of the universe without time, and thus without the effect of MOTION as one traversed these many different reference frames (galaxy, solar system, planetary orbit, rotating planet, etc).An analogous result obtains when considering even mechanical motion and time: Motion through space (x,y,z, or r, theta, phi, or x1, x2, x3) sacrifices motion through time (ct, or x4) such that the interval through space-time (x1, x2, x3, x4) is always unchanged; invariant. This is how the measurement of time becomes relative. Motion through time is contracted to compensate for the motion through space, keeping the interval invariant.Both the Electrodynamic Field and the Gravitational Field are Gauge Fields.Another principle that bent my brain Landau covers in paragraph 95: The equations of the gravitational field also contain the equations for the matter which produces said field.From which the central conclusions may be deduced.Matter is FieldField and matter do not really fill space, like we all intuitively think. Rather, empty space has no objective measurable reality.As Einstein put it: "There is no space empty of field"Thus: Field..... is..... Space

I have read the old version in French which was very concise and the new one is even more concise.Landau & Lipchitz do not need recommendation as I think they are the best books I know of.I recommend the book of Field Theory to those who already are knowledgeable and who would like to add a high level overview on the field theory (including Relativity).This overview goes in parallel with a deep insight on the various aspects of the theory.(I also very strongly recommend Vol1 : Classical Mechanics of the same authors)

Elsevier has made a travesty of this classic work. The good news is that unlike some other volumes in this series (like the completely illegible vol. 3 which I also left a one-star review on), this 2010 digital edition is crisply printed, so some of the other 1-star reviews on this edition complaining about the print quality are no longer applicable. The bad news is, they seem to have gotten it crisp by running some older, barely-legible edition through OCR and then failing to correct typos, so now instead of being hard to read, many equations are crisply *wrong*. The photos show a couple examples. In the footnote on page 18, the subscript indices in the bottom-right equation should be "pklm", not "prlm". Equation 9.3 contains *two* typos: the exponent should be 3/2, not 1/2, and the plus sign before dv/dt should be a multiplication.This material is challenging enough already without having to battle through Elsevier's OCR slop every handful of pages.

It's so simple to read and just to the point. I honestly had to use the Jackson book, which was not that great, but made a great grade because of the Landau-Lifshitz classic. Then there was the advanced MIT EM book which made so much more sense, but it was all math. Those 3 books alone will give you a pretty adequate understanding of EM, enough to make over 95 out of 100 on every assignment. The Landau, MIT book together are well pretty cool themselves.

The printing quality is not very good, especially when this book contains so many formulas. Some subscripts are not recognizable.