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 do I obtain the low energy supergravity actions from the 5 superstring theories?
In Domain-Walls and Gauged Supergravities by T.C. de Witt, there is a small table giving the 5 string theories and each of their effective sugras. I am looking for detailed reviews of how these sugras ...
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Derivation of the Noether current (Gauss law operator) in anomalous chiral gauge theory
I am reading Fujikawa-Suzuki's Path Integrals and Quantum Anomalies, §6.3. The Lagrangian I am looking at is
\begin{equation}
\mathcal{L}=-\frac{1}{4g^2}\left(\partial_\mu L_\nu^a-\partial_{\nu}L_\mu^...
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In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?
Here are the equations. ($V$ represents a potential function and $p$ represents momentum.)
$$V(q_1,q_2) = V(aq_1 - bq_2)$$
$$\dot{p}_1 = -aV'(aq_1 - bq_2)$$
$$\dot{p}_2 = +bV'(aq_1 - bq_2)$$
Should ...
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2
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Meaning of $d\mathcal{L}=-H$ in analytical mechanics?
In Lagrangian mechanics the momentum is defined as:
$$p=\frac{\partial \mathcal{L}}{\partial \dot q}$$
Also we can define it as:
$$p=\frac{\partial S}{\partial q}$$
where $S$ is Hamilton's principal ...
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Prerequisites for studying Lev Landau Mechanics vol. 1 [closed]
Lev Landau Mechanics vol. 1 dives directly into Lagrangians and Hamiltonians. What do you think are the prerequisites in order to study and grasp it?
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Unitary Gauge Removing Goldstone Bosons
The Lagrangian in a spontaneously broken gauge theory at low energies looks like
$$ \frac{1}{2} m^2 ( \partial_\mu \theta - A_\mu )^2 $$
and the gauge transformations look like $\theta \rightarrow \...
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3
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How can the stress-energy tensor $T^{μν}$ be unique when the Lagrangian $L$ is not?
A relation (or definition) between the stress-energy tensor and the Lagrangian in GR is routinely seen:
$$T^{μν} = -2 \frac{∂L}{∂g_{μν}} - g^{μν} L \quad\quad(*)$$
(or some variation of this, ...
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1
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Volume preserving transformation in the Circular Restricted Three-Body problem
the Lagrangian of the planar circular restricted three-body problem in the rotating coordinate frame is:
$$\mathcal{L}(x,y,\dot{x},\dot{y})=\frac{1}{2}(\dot{x}-\Omega y)^2 + \frac{1}{2}(\dot{y}+\Omega ...
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Robin conditions from action principle
Consider the Lagrangian density
$$L(\tilde{\phi}, \nabla \tilde{\phi}, \tilde{g}) = \tilde{g}^{\mu \nu} \nabla_{\mu} \tilde{\phi} \nabla_{\nu} \tilde{\phi} + \xi \tilde{R} \tilde{\phi}^2$$
with $\...
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How to add a non-chiral lepton doublet to the Standard Model?
How would the Standard Model Lagrangian (before symmetry breaking) change if we were to add a non-chiral lepton doublet $\ell_{L,R}$ with weak hypercharge $y=-\frac{1}{2}$ to the $SU(2)\times U(1)$ ...
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Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution?
This is from Analytical Mechanics by Louis Hand et al. The proof is about Maupertuis' principle. The author seems to say that Hamilton's principle allow a path to have both a process of time forward ...
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Stress-energy tensor in terms of the Lagrangian [closed]
In Dirac's "General Theory of Relativity" (Chap 30) he gets
$$T^{μν} = -\frac{2}{√} \frac{∂\mathscr{L}}{∂g_{μν}}$$
where $\mathscr{L}$ is the Lagrangian density and $√$ means $\sqrt{-g}$.
$\...
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What notation in physics is used to describe the transfer of kinetic energy from one particle to another particle? [closed]
I've being practicing Lagrangian mechanics and stumbled upon the problem of the so-called famous physical experiment "Newton's cradle". I'm able to define the equations of motion regarding a ...
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How do you differentiate $F^{αβ}$ with respect to $g_{μν}$?
I want to experiment with this relation (from Dirac's "General Theory of Relativity"):
$$T^{μν} = -\left(2 \frac{∂L}{∂g_{μν}} + g^{μν} L \right)$$
using the electromagnetic Lagrangian $L = -(...
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Path of a free particle over a sphere [closed]
So I was trying to see if I can prove in any way that the path that follows a free particle moving on the surface of a sphere was a circumference over the sphere, so my approach was this.
I have the ...
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