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.
5,654 questions
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Addition or disappearance of symmetries due to a particular field transformation [closed]
I have a question related to symmetries in field theory... I request someone to please help me with it:
Let us have an action $$S= \int d^4 x \mathcal{L}(A,B) $$ of fields $A,B$. Suppose we make a ...
- 445
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Transformation to linearise action over time
Let a body $m$ be in motion such that it follows the path of least action. We can define the total action of this body by computing $$S=\int_{t_0}^{t_f}T_m-V_m\,dt.$$ Furthermore, we can define action ...
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Does Charles Kittel's explanation of the canonical momentum in an electromagnetic field sense?
In appendix G of Charles Kittel's book on the introduction into Condensed Matter Physics an explanation of the canonical momentum in an electromagnetic field is provided:
The motion of a charged ...
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SUSY QM as point-particle limit of Superstrings
There is a pretty clear resemblance between the Lagrangians for SUSY QM (1-dim susy sigma model) and various superstring theories (2-dim susy sigma models).
Again intuitively, one should expect the ...
- 538
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How the vacuum expectation value of $\sigma$ is related to the tadpole diagram?
In Peskin & Schroeder's book, they introduce the linear sigma model with a Lagrangian (chapter 11.1,p349)
$$
L = \frac{1}{2} (\partial_\mu \phi^i)^2 + \frac{1}{2} \mu^2 (\phi^i)^2 - \frac{\lambda}{...
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Why can you not take $u \cdot u = c^2$ in the relativistic free massive particle Lagrangian?
In my classical electrodynamics class, we use the Lagrangian of the relativistic free massive particle as $$L = - mc\sqrt{\dot{r}\cdot\dot{r}}.$$ Where $\dot{r}^\mu = u^\mu = \frac{dr^\mu}{d \tau}$; $...
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Generic form of the matter Lagrangian in QFT
It seems to me like any sensible matter Lagrangian must obey the following constraints:
It must be invariant with respect to local $SU(N)$ transformations, diffeomorphisms of the space-time manifold, ...
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In particle physics, what is the *motivation* to have invariance of a defined Lagrangian under a transformation of phase $e^{i\alpha}$ of the fields?
In particle physics, one checks the invariance of the Lagrangian under global transformations of the fields $\psi\rightarrow e^{i\alpha}\psi$ and local transformations $\psi\rightarrow e^{i\alpha(x)}\...
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Is the single-particle relativistic Lagrangian really reparameterization invariant?
The relativistic Lagrangian for a single massive particle is given by (up to a proportionality constant)
$$ L = \sqrt{-g_{\mu\nu} U^{\mu} U^{\nu}} $$
where $U^{\mu} = d X^{\mu} / d \tau$.
It can be ...
- 83
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Formulating the catenary problem as a variational problem
I am interested in studying the curve a string follows when fixed by two points and subject to a (uniform) gravitational field. Say the string has a constant length $L$ and is fixed on two points A, B ...
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Physical Description of a Coin. Equations and constraints
I've been trying to describe the behaviour of a coin that can roll, spin and fall with Lagrangian Mechanics. The coin can roll without slipping with it's only "knowledge" of the floor being ...
- 1,843
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How to determine the number of Goldstone bosons in my theory?
I have a BSM model where we consider for our scalar tree level potential a Higgs doublet, $\Phi$, and a dark $SU(3)$ triplet, $\Psi$ (scalar field), given by:
$$V(\Phi,\Psi) = \lambda_1(\Phi^*\Phi)^2 +...
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Extra terms for electromagnetic stress-energy tensor?
I am using the following Lagrangian density for classical electrodynamics.
\begin{align*}
\mathcal{L} &= -\frac{1}{4\mu_0} F^{\mu\nu} F_{\mu\nu} + J^\mu A_\mu
\end{align*}
This gives 2 of ...
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On gauge theories and redundant degrees of freedom
Given an action or Lagrangian with the additional information that it is a gauge system, how do we know this field has how many physical or redundant degrees of freedom? Is there any systematic method ...
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Difficulty of Interpretation of Conjugate Momentum as a Generator of Field, QFT
There is an idea which claims that the commutation relation
$$
[ \phi(x,t), \pi(x',t) ] = i\hbar \delta^3(x - x')
$$
implies that $\pi$ is the Generator of $\phi$.
At first, this seemed reasonable to ...
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