Classical field theory Definition and 31 Threads

Hi, I'm currently taking a class in Classical Field Theory. We've covered topics such as relativity, Poincaré and Lorentz groups, tensor algebra and calculus, as well as Lie algebras and groups. I would like to review for my exam and was wondering if anyone has practice questions or past exams...

So, recently I've been working through "Classical Theory of Gauge Fields" by Rubakov. I've more-or-less been able to do the exercises as they've come up, but every once in a while I feel like I'm symbol pushing to get the correct answer, or ignoring certain confusions I have in favour of doing...

I've been reading about the form of the energy momentum tensor for a polarizable medium in electromagnetic fields and i'm not sure if there is a scientific consensus on its form. Starting from the series of papers by Kluitenberg in the 1950s to works by Israel and Dixon in the 70s... various...

Let's say I have the following situation $$I = \dfrac{\partial}{\partial x^{\alpha}}\int e^{k_{\mu}x^{\mu}} \;d^4k$$ Would I be able to commute the integral and the partial derivative? If so, why is that? In the same line of thought, in the situation I'm able to commute, would the result of...

Varying ##\partial_\lambda\phi\,\partial^\lambda\phi## wrt the metric tensor ##g_{\mu\nu}## in two different ways gives me different results. Obviously I'm doing something wrong. Where am I going wrong? Method 1: \begin{equation} (\delta g_{\mu\nu})\,\partial^\mu\phi\,\partial^\nu\phi...

Let us consider an action ##S=S(a,b,c)## which is a functional of the fields ##a,\, b,\,## and ##c##. The solution of the field ##c## is given by the expression ##f(a,b)##. On taking into account the relations obtained from the solutions for ##a## and ##b##, we find that ##f(a,b)=0##. If the...

If a Lagrangian has the fields ##a##, ##b## and ##c## whose equations of motion are denoted by ##E_a, E_b## and ##E_c## respectively, then if \begin{align} E_a=f_1(a,b,c)\,E_b+f_2(a,b,c)\,E_c \end{align} where ##f_1## and ##f_2## are some functions of the fields, if ##E_b## and ##E_c## are...

Hi, I am trying to learn relativistic classical field theory as a preparation for studying quantum field theory. I am currently reading chapter 13 i Herbert Goldstein's Classical Mechanics edition 3, but I think that this book is a bit too brief and does not fully derive and explain the...

I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned that one could obtain the dilaton monopole interaction as such: where the action is given by However, I...

From this post-gradient energy in classical field theory, one identifies the term ##E\equiv\frac{1}{2}\left(\partial_x\phi\right)^2## as the gradient energy which can be interpreted as elastic potential energy. Can one then say that $$F\equiv -\frac{\partial...

1.) The rule for the global ##SO(3)## transformation of the gauge vector field is ##A^i_{\mu} \to \omega_{ij}A^j_{\mu}## for ##\omega \in SO(3)##. The proof is by direct calculation. First, if ##A^i_{\mu} \to \omega_{ij}A^j_{\mu}## then ##F^i_{\mu \nu} \to \omega_{ij}F^j_{\mu\nu}##, so...

On examining Maxwell's third equation which is about time varying magnetic fields (Faraday's electromagnetic induction) we find that time varying magnetic fields produce loops of electric fields in space irrespective of whether a coil is present or not, if any coil is present then these loops of...

hi, I'm currently taking a classical field theory class (electromagnetism in the language of tensors and actions and etc) and we have just encountered the gauge symmetry, that is for the 4 vector potential we can add a gradient of some smooth function and get the same physics (if we take Aμ →...

When a classical field is varied so that ##\phi ^{'}=\phi +\delta \phi## the spatial partial derivatives of the field is often written $$\partial _{\mu }\phi ^{'}=\partial _{\mu }(\phi +\delta \phi )=\partial _{\mu }\phi +\partial _{\mu }\delta \phi $$. Often times the next step is to switch...

Hi everyone, I have a question that, when came to me, sounded a bit silly to me as well, but then I realized, I myself maybe don't understand the logic behind this 100%, so why not discussing with you about it. So my question is the following. Usually we are used to do quantum field theory...

Hi, i would be curious to know what would be the prerequisites for learning the classical field theory !

In field theory a typical Lagrangian (density) for a "free (scalar) field" ##\phi(x)## is of the form $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi -\frac{1}{2}m^{2}\phi^{2}$$ where ##m## is a parameter that we identify with the mass of the field ##\phi(x)##. My question is...

In classical field theory, translational (in space and time) symmetry leads the derivation of the energy-momentum tensor using Noether's theorem. From this it is possible to derive four conserved charges. The first turns out to be the Hamiltonian, and thus we have energy conservation. The...

In classical field theory, the field, φ, is usually constructed from a very large number of coupled harmonic oscillators. Let's say our φ consists of just electrons. What does φ best represent physically, a very large number of electrons or can it represent just a few electrons? Which is the...

Homework Statement In this problem, you will calculate the perihelion shift of Mercury simply by dimensional analysis. (a) The interactions in gravity have ##\mathcal{L}=M^{2}_{Pl}\Big(-\frac{1}{2}h_{\mu\nu}\Box...

Homework Statement A class of interesting theories are invariant under the scaling of all lengths by ##x^{\mu} \rightarrow (x')^{\mu}=\lambda x^{\mu}## and ##\phi(x) \rightarrow \phi'(x) = \lambda^{-D}\phi(\lambda^{-1}x)##. Here ##D## is called the scaling dimension of the field. Consider...

Homework Statement Given the Maxwell Lagrangian ##\mathcal{L} = -\frac{1}{2} (\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu}) + \frac{1}{2} (\partial_{\mu}A^{\mu})^{2}##, show that (a) ##\frac{\partial \mathcal{L}}{\partial (\partial_{\mu}A_{\nu})} = -...

Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...

One page 24 of his book on classical field theory (4th edition), Landau derives the relativistic equation of motion for a uniformly accelarated particle. How does he get the differential equation that leads him to his result?

There's very few problems in Landau's books. I'm the kind of guy that properly learns material by doing tons of problems. Of course I can pull from other textbooks but there's the issue of different notation, extra material within chapters, etc... Does anyone know of a good resource that can...

Hey everyone, I posted this a while back in General Physics without any reply, and it looks like this is actually the germane forum (despite the fact that I'm explicitly NOT looking for QFT) -- but I couldn't find the "move thread" option... Anyway: I'm looking for some books that...

Homework Statement Could someone please explain what is meant by the term: \partial_{[ \mu}F_{\nu \rho ]} Homework Equations I have come across this in the context of Maxwells equations where F^{\mu \nu} is the field strength tensor and apparently: \partial_{[ \mu}F_{\nu \rho...

Classical Field Theory without Force Has anyone seen how this has been approached?

Hi, I have a problem in classical field theory. I have a Lagrangian density \mathcal{L}=\frac{1}{2}\partial_\lambda \phi \partial^\lambda \phi + \frac{1}{3}\sigma\phi^3 . Upon solving the Euler-Lagrange equation for this density, I get an equation of motion for my scalar field \phi (x), where...

Hello, I'm looking to get a book on classical field theory at a beginner level, so please don't recommend anything that a first year grad student wouldn't understand! Anyways I was look into getting Landau and Lifgarbagez's book any other suggestions? I don't really have any idea of which...

Hello folks, I would like to know more about the standard books in Classical Field Theory which I am not really familiar with. I would be grateful if you suggest something (be it a book/lecture notes etc...) in line with the 2nd chapter of the following lecture notes...