# Tagged Questions

For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.

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### Feynman rules from interaction Lagrangian with electromagnetic tensor (vertex)

I am currently studying for my QFT exam and in particular learning the methods of reading the Feynman rules directly off the Lagrangian. However, I'm still a bit uncertain how to deal with ...
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### Is there an action for every physical law?

Given an action, I can get the differential equation governing the evolution of the system by applying the principle of least action. Does it work the other way around? Given any differential ...
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### How to find propagator from Lagrangian at a glance?

If I have a Lagrangian in momentum space of the form $$\mathcal{L} = W_\mu^{ \dagger}(p)f(p)^{\mu \nu}W_\nu(p)$$ how is the propagator for the field related to the function $f(p)$ (e.g. is it ...
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### What is the Green's function of the Klein-Gordon equation with a variable mass?

Usually, the Klein-Gordon equation's propagator is calculated with a constant mass. But what if the mass is a variable? That is, $$(-\partial^2 + m(x)^2)G(x, y) = \delta^4(x-y)$$ where $m(x)$ is a ...
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### Action and equation of motion for codim-2 “cosmic” brane in Einstein gravity, in 3d

Consider the following action, $$S = S_{EH} + S_{B} = -\frac{1}{8\pi G_N}\int d^3 X \sqrt{G}R + T \int dy \sqrt{g} ,$$ where, $G_{\mu \nu}$ is the bulk metric, and $g$ is the induced metric on the ...
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### Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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### Multiplying Lagrangian by a constant

Does a Lagrangian of a system multiplied by an arbitrary constant still work? If if I apply the Euler-Lagrange equations, do they still guarantee that the action is extremal? I arrived to the ...
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### Scalar fields in AdS$_3$

I'm looking at lecture notes on AdS/CFT by Jared Kaplan, and in section 4.2 he claims that the action for a free scalar field in AdS$_3$ is S=\int dt d\rho d\theta \dfrac{\sin\rho}{\cos\rho}\dfrac{1}...
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### Help with relativistic notation (Derivative of Lagrangian)

I am trying to learn QFT, but I haven't taken a course in general relativity so the relativistic notation stuff is taking me a bit to get used to. I do not understand how to do the following. For a ...