# 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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### 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" ...
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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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### 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 ...
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### Fourier expansion of positive and negative fields in In-In formalism

Recently, I am reading articles regarding In-In formalism, Schwinger-Keldysh formalism. One advantage of this formalism is it is easy to construct the expectation values of operators in-state without ...
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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 ...
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### Two constraints of $\bar\psi$ from equations of motion for Free Dirac Field Lagrangian

$$\mathcal{L}=\bar\psi(i\gamma^\mu\partial_\mu-m)\psi,$$ taking Euler-Lagrange equation on $\bar\psi$ gives the more familiar Dirac equation $$(i\gamma^\mu\partial_\mu-m)\psi=0$$ and its adjoint ...
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### Second-order perturbation in Brans-Dicke gravity

Let be $g_{\mu \nu} = \eta_{\mu\nu}+h_{\mu\nu}$ the perturbation of the metric and $\phi=\phi_0 + \varphi$ the perturbation of a field. The lagrangian of a scalar-tensor theory of gravity is: \...
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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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### 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 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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### Geodesics: Energy functional vs length functional

The Wikipedia article about geodesics talks about the equivalence of obtaining the geodesic by either minimizing the length functional $L$, or by minimizing the energy functional $L^2/2$, cf. the Phys....
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### Dirac's pseudo-energy tensor

Having trouble with Dirac's eq. (31.3) ("General Theory of Relativity"). Probably a simple math question, but I need to provide a little background on the symbols. Dirac defines the pseudo-...
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### Reference request for QFT $SO(3)$ non-linear sigma model

I was wondering if anyone has a reference that could help me understand quantum field theories that have a nonlinear configuration space. For example, from classical mechanics if we have a three-...
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### Why does the Lagrangian not show particle-interaction? Why are normal/tension forces not considered?

(1) For formulating a lagrangian for a system of particles compared to one free particle, we start with the kinetic energy and formulate a potential energy term that is in terms of each of the radius ...
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### Coleman-Weinberg mechanism at two-loop

I'm trying to understand how to perform the CW mechanism (http://www.scholarpedia.org/article/Coleman-Weinberg_mechanism) to scalar theories at two-loop order. More specifically how to find the ...
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In my mechanics class, I learned that the components of the generalized force, $Q_i$, could be calculated using: \begin{equation}\tag{1}Q_i = \sum_j \frac{\partial \mathbf{r}_j}{\partial q_i}\cdot \...