# 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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### Magnetic monopoles in field theory

In standard QED, we couple the electron to electromagnetism by replacing $$\partial_\mu \to \partial_\mu + i e A_\mu.$$ Upon taking the classical limit, we find that this gives electrons an electric ...
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### Lagrangian Interaction Type and Spin-Dependence

So I'm transitioning from reading particle physics books to the literature, specifically as it pertains to dark matter models. In this case I'm talking about t-channel DM-nucleon scattering. They ...
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### Problem obtaining string equations from Polyakov action [closed]

I am trying to obtain the string equations of motion from the Polyakov action in the conformal gauge, i.e.: $$S=T\int{d\tau d\sigma (\dot{x}^2-x^{'2})}\equiv\int{d\tau d\sigma \mathcal{L}}$$ where ...
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### The components of applied forces on the masses of a Trebuchet

Background information: I was following an online mechanics document in order to learn how to derive the equations of motion for a trebuchet (shown below) using Lagrangian mechanics. At some point ...
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### Number of degrees of freedom in the Standard Model Lagrangian

Consider a Lagrangian $L$ which depends on a number of fields $F_1$, $\cdots$, $F_N$ and their (spacetime) derivatives. Each of those fields $F_n$ is valued in $\mathbb{R}^{k_n}$. Is the Standard ...
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### Lorentz transformation and symmetries of the Lagrangian [duplicate]

Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations ...
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### Partial Differentiation without chain rule in Euler Lagrange Equations [duplicate]

The Euler-Lagrange equations for a bob attached to a spring are $$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial v} = \frac{\partial L}{\partial x}$$ But $v$ is a function of $x$. Is it ...
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### Derivation of Lagrangian [duplicate]

Actually I am beginning to study Lagrangian and Hamiltonian Mechanics. The book that I am considering directly introduces the Lagrangian L=T-V. Though further on the book , the Euler Lagrange ...
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### Classical dynamics of a matrix

For a system of interacting particles, we can formulate Hamiltonian dynamics in terms of a vector of position coordinates $q$ and a vector of momentum coordinates $p$. Then the Hamiltonian takes the ...
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### Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
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### How do I find the linear components of acceleration in a pendulum?

I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to ...
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### How are Lagrangians in QFT constructed?

Various particle equations (like the K-G equation, the Dirac equation, the Proca equation etc.) in QFT are derived by applying the Euler-Lagrange equations to the Lagrangian density. But how are these ...