# 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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### Is the angular momentum conserved? 2 [closed]

I have a Lagrangian equation and an expression for the generalized momenta, if I put the generalized momenta into the Euler-Lagrange equation and I get a differential equation as result, does that ...
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### Calculations with co- and contravariant formalism in QFT

i have another question regarding calculations with the co- and contravariant formalism in QFT. It is not that i don't understand all of this, but most of the time i'm missing some "middle" ...
1 vote
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### What is the full QED Lagrangian with physics units written out?

I wonder what the QED Lagrangian would look like if you carefully write out all units of the terms and make sure they are consistent. I think there is something missing about Coulomb. Can you write ...
1 vote
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### Semi-classical limit of Feynman path integral

I am reading Blau's note on The Path Integral Approach to Quantum Mechanics. I am troubled for the derivations of semi-classical limit of Feynman path integral, which is located on Page.50 of Blau's ...
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### Why do we put factors of zero in a Lagrangian that is to be extremized?

According to the Wikipedia page on Lagrange multipliers under the section - Example 3: Entropy, it is written that: $$f(p_1,p_2,\ldots,p_n) = -\sum_{j=1}^n p_j\log_2 p_j$$ For this to be a ...
1 vote
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### Derive Linearized Einstein's equation from Lagrangian approach

Given the Hilbert action: $$S_{H}=\int \sqrt{|g|}R d^{n}x$$ and the metric written in terms of Minkowski and perturbed metric: $$g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu}.$$ I am able to derived the ...
1 vote
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### Noether's theorem derivation by Greiner

I'm reading Quantum Mechanics (Symmetries) by Greiner, in the topic of Noether's theorem (pp. 6-7) there are points where it is a little bit confusing. I'll add a link to the google book version so as ...
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### Hoop and Pulley lagrange [closed]

With respect to the problem raised, I have doubts if obtaining the characteristic equations are appropriate, or I made a mistake in some step to obtain them, since I have had problems all week to be ...
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### Wilsonian RG and Effective Field Theory

I'm having trouble reconciling the discussions of the Wilsonian RG that appear in the texts of Peskin and Schroeder and Zee on the one hand, and those of Schwartz, Srednicki, and Weinberg on the other....
1 vote
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### How do equations of motion in BF theory imply triviality of powers of observables?

Following the lectures of Nathan Seiberg at PiTP in 2015 https://www.youtube.com/watch?v=pqgNrVTQ4yM&t=666s, consider $U(1)$ BF theory in 2D $$S(B,A)=\frac{n}{2\pi}\int_\Sigma B\text{d}A,$$ and ...
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### Equation of motion for scalar field in Brans-Dicke Theory [closed]

The action is given by S=∫▒〖d^4 x〗 √(-g) {(F(φ))/2 R-1/2 ∇_c φ∇^c φ-V(φ)}+S_m I am trying to vary with respect to ϕ using Euler - Lagrange equations in curved spacetime, to get this ▢φ+3φ ̇H+ V_φ=1/2 ...
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### How do I understand the Hodge $⋆$ operator in Yang-Mills Lagrangian?
The gauge-invariant part in Yang-Mills Lagrangian is $$\mathcal{L}_{\text{gauge}} = -\frac{1}{2}TrF_{\mu\nu}F^{\mu\nu} = -\frac{1}{4}F_{\mu\nu}^aF^{a, \mu\nu}.$$ Sometimes I see the lagrangian ...