# Questions tagged [lagrangian-formalism]

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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### How to get the Magnetic Force from the Electromagnetic Tensor using Hodge Decomposition?

The following notation is used below: d: exterior derivative $\delta$: codifferential (adjoint of d) $\times$: skew-symmetric operator of a $\mathbb{R}^3$-vector $\nabla\times$: Curl operator in ...
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### Deducing equation of motion for a free particle using the form of the Lagrangian

This is in reference to the question: Deriving the Lagrangian for a free particle My question is specifically in regards to QMechanic's answer to this question, and I have quoted the relevant part of ...
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### Field shift in free Klein-Gordon theory

I am reading Peskin & Schroeder Ch9 and am stuck on a calculation going from equation 9.36. The problem is essentially a change of variable of a Klein-Gordon field. Beginning, we have an integral ...
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### Euler-Lagrange Equation, $\dot{P_{\alpha}}\neq\partial_{q_{\alpha}}L$

We know \begin{equation} \frac{d(\partial_{\dot{q}_{\alpha}}T) }{dt}=\partial_{q_{\alpha}}(T-U) \\ \partial_{\dot{q}_{\alpha}}U=0 \rightarrow\dot{P_{\alpha}}=\partial_{q_{\alpha}}L \end{equation} ...
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### Charge of antifermions in 1+1d QED, and in 1+1 CED

NEW REPRHAISING OF THE QUESTION: Is it possible that in 1+1d QED the negative charge of the $\psi^\dagger$ fields appears only in the quantum model when we introduce the commutator relation for ...
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### Should rotation of a rigid body confined to a sphere couse it to divert from a big circle?

Consider an axially symmetric body constrained to a unit sphere in such a way that the symmetry axis of the body is always normal to the sphere. Edit: I guess what I really wanted to ask (although it ...