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.

2,587 questions
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Why is an action built from superfields guaranteed to be supersymmetric?

Given a superfield (in 0+1 spacetime + 2 superspace coordinates) $$X(t,\theta_1,\theta_2) = x(t) + \theta_i \psi_i(t) + \theta_1 \theta_2 F_{12}(t)\tag{1}$$ and given the standard supercharges ...
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Is there any reason that Landau and Lifshitz don't discuss Noether's theorem in their mechanics book? [on hold]

I'm currently working my way through the Course volume one. Unless I've completely missed it, the authors omit any discussion of Noether's theorem, instead deriving various conservation laws on a case ...
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Energy-Momentum tensor in Yukawa theory

Given the following Lagrangian: $$\mathcal{L}=\frac 1 2\left(\partial_{\mu} \phi \partial^{\mu} \phi-M^{2} \phi^{2}\right)+\overline{\psi}(i \not \partial-m) \psi+g \phi \overline{\psi} \psi$$ How ...
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Solving the Euler-Lagrange equation with the Axion Lagrangian

I am trying to show that for a constant axion field $\theta(\textbf{x},t)=const.$ the axion Lagrangian $\mathcal{L}_\theta=-\frac{\kappa\theta}{4\mu_0}F_{\mu\nu}\tilde{F}^{\mu\nu}$ does not lead to a ...
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Deriving the stress-energy tensor from the Einstein-Hilbert action

I'm a mathematician who knows very little physics and is trying to learn relativity theory from a mathematical perspective. Let $M$ be a compact, orientable manifold. In the vacuum, the Einstein-...
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Independents fields and the Lagrange Density of Schrodinger equation [duplicate]

I have a doubt about the lagrangian of the Schrodinger equation. If we consider the wave function $\psi(\textbf{x},t)$ that satisfy the Schrodinger equation as a field, one way of construct the ...
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Gravitons and self-interaction

In the book quantum field theory and standard model by Schwartz, there is a problem 9.4 that says by considering lorentz invariency of compton scattering, you can prove that for spin 1 field there ...
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The Lagrangian for gravitational potential energy in a double pendulum

For a double pendulum what would be the gravitational energy. I am trying to work out the Lagrangian for the double pendulum. I got the kinetic energy but I am struggling on the gravitational ...
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Experimental methods to identify C.O.G of a highly heterogeneous cube

While taking to a college about calculating the centre of gravity of multibody basic objects, the question was raised on how one would determine the C.O.G of a highly heterogeneous object of a given ...
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Acceleration due to central forces in the Lagrangian

On Wikiversity it states that for central forces: Wouldn't $\ddot{\vec{r}}_1$ be the same as $\vec{g}$?
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Does it make sense to say that the action is even or odd under time reversal?

The action of a system in mechanics is an integral over time defined as $$S[x(t)]=\int\limits_{t_1}^{t_2}L(x,\dot{x},t)dt.$$ Here, the time $t$ is integrated making the left hand side depend only on ...
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Swinging Atwood and Hoop And Pulley Lagrangian

The picture is showing the swinging atwood and a hoop and pulley. I know the lagrangian for both two, I have no problem with the kinetic energy of both but i couldn't convince myself that for the ...
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Rotating coordinate frame

Hello I have a question about rotating coordinate frames. Following the book of Brizard the Lagrangian is given by \begin{equation} L(\mathbf{r}, \mathbf{\dot{r}}) = \frac{m}{2} \vert \mathbf{\dot{r}} ...
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I was looking for help in order to proove 2 relations that Goldstein has put in his book. $$L(q, \dot{q}, t)=L_{0}(q, t)+\tilde{\mathbf{\dot{q}}} \mathbf{a}+\frac{1}{2} \tilde{\boldsymbol{\dot{q}}} \... 1answer 41 views Doubts in an introduction to classical field theory I started to study classical field theory using the book "Field Quantization" of Greiner and Reinhardt, and I have some doubts. First, the book write the Lagrangian L(t) as a functional of a field \... 0answers 55 views Anderson-Higgs Mechanism Consider an abelian gauge field coupled with a complex field:$$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D\varphi)^\dagger D\varphi+\mu^2 \varphi^\dagger\varphi-\lambda(\varphi^\dagger\varphi)^2.$... 0answers 107 views Explicit counting of gauge field degrees of freedom Consider a connection on a principal$U(1)$-bundle$A_\mu$over the flat base manifold$M_4$. The action of the theory is described in terms of the curvatures of such connection coupled to some source ... 0answers 28 views How do interaction terms appear in the Lagrangian? How does forcing the Lagrangian to be invariant under$U(1)$group give rise to the electromagnetic interaction term? 1answer 39 views Velocity of particle in non-inertial frame [closed] Can velocity of the free particle remain constant in non-inertial frame as contrast to free particle in an inertial frame? I know the answer is straightforward yes but taking a different perspective ... 0answers 28 views Noether current Lorentz rotation massive vector field I'm considering a massive vector field in classical field theory. With the Lagrangian density $$\mathscr{L}=-\frac{1}{4}V^{\mu\nu}V_{\mu\nu}+\frac{1}{2}m^2V^{\mu}V_{\mu}.$$ I want to prove from the ... 1answer 65 views Why is there a Lagrangian? [duplicate] In all discussions regarding the Lagrangian formulation it has always been said that$L = T - V $, only is a correct guess that when operated via through the Euler -Lagrange equation yields something ... 1answer 32 views On the use of Lagrange multipliers in deriving the Lagrange eqn. in classical mechanics Can one derive the Lagrange eqn based on the methods of Lagrange multipliers? That is, we need to minimize the action with respect to the trajectory keeping the net energy of the body in motion ... 1answer 79 views Is it there any relation between an action and entropy? I've found papers that seem to suggest that these concepts are the same, like this one: https://arxiv.org/abs/1005.3854 But I've found answers in Physics Stack Exchange that say that both are ... 1answer 52 views How to calculate the conserved energy$E$from the Lagrangian? I am reading a PhD thesis that considers the Lagrangian $$\mathcal{L}=\partial_\mu\phi\partial^\mu\phi^\star-U(|\phi^2|)$$ where$\phi$is a complex scalar field and$U(|\phi|^2)\$ is an arbitrary ...
I'm trying to find a suitable Lagrangian for a damped harmonic oscillator, a system that satisfies the following equation of motion: $$m \ddot{x} + \gamma \dot{x} + \frac{d\phi}{dx} = 0.$$ What I ...