# Tagged Questions

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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### Noether's Theorem and scale invariance

Noether's theorem usually considers coordinate/field transformations which leave the Lagrangian invariant up to a divergence term, i.e. $\mathcal{L} \rightarrow \mathcal{L} + \partial_{\mu}f^{\mu}$ ...
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### Lagrangian of a coupled pendulum

I am trying to find the Lagrangian for a coupled pendulum: the two pendulums have the same characteristics (length $l$ and mass $m$) and are attached to the same roof at a distance $d$. In addition, ...
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I am self-studying Goldstein's book "Classical Mechanics", and I need some help understanding the part where Goldstein discusses using Hamilton's principle to solve systems with holonomic constraints (...
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### What is difference between variations of the work and virtual work?

I really want to know whether or not both equations are the same mathematically. I think that they are the same, I just want to be sure. (Reference: this website.)
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### Flavour basis to mass basis

I am not really understood why we need to change the basis from flavour basis to mass basis after Spontaneous symmetry breaking applying to Yukawa Lagragian? why we can't take (or not making ...
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### Legendre transform

How do they obtain this? $$g(x, y, u) = ux − f(x, y)$$ Is in page 3 after eqn 4.4.
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### Learning about 4 topics in physics [closed]

This isn't really a question on any of those numerous underlying concepts behind the various sub-disciplines of physics, but hear me out: I'm still in Higher Secondary, but I'd really love to know ...
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### Question in Lagrangian formalism

In lagrangian mechanics, where $L=T-U$ and the lagrangian formulation is $\frac{d}{dt}\big( \frac{\partial L}{\partial \dot{q_i}}\big)-\frac{\partial L}{\partial {q_i}}=F_i$, where $F$ is the non-...
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### Matching symmetry factor when a heavy vector field is integrated out

Let us consider the lagrangian $$\mathcal{L} = \alpha \bar{u}\gamma^\mu u V_\mu + \frac{\beta^2}{2}V_\mu V^\mu$$ there $V_\mu$ is a heavy vector field and $u$ is a massless SU(3)-colored quark. If ...
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### Lagrangian of classical electromagnetism without $A_{\mu}$ field [duplicate]

Is there a Lagrangian reproducing Maxwell's equations without the use of the scalar and vector potential? Obviously $\mathcal{L} = -\frac14F_{\mu \nu}F^{\mu \nu}$ doesn't work since in terms of $E$ ...
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### Lagrangian mechanics not relying on time or independent of time [closed]

If neither the potential energy nor kinetic energy depends on time, then Lagrangian is explicitly independent of time I find this statement a little bit odd because velocity is distance over time or ...
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### Connection between “classical” Grassmann variables and Heisenberg Equation of motion

I have been reading di Francesco et al's textbook on Conformal Field theory, and am confused by a particular statement they make on pg 22. Let $\{\psi_i\}$ be a set of Grassmann variables. Starting ...
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### Non-canonical transformation

I would like to know any method to transform a known non-canonical set of variables to a canonical set for a given system. The Lagrangian and Hamiltonian are known in the non-canonical variables. I ...
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### From gauge invariance to charge conservation in covariant electrodynamics

I tried to solve the equations of motion using the action for the electromagnetic field interacting with a current, like $$L = F_{\mu\nu}F^{\mu\nu} + A_{\nu}j^{\nu}$$ getting the right Maxwell's ...
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### Lagrangian of an effective potential

If there is a system, described by an Lagrangian $\mathcal{L}$ of the form $$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$ where $T$ is the kinetic ...
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### A question about Euler-lagrange equations

This question passes my mind so often, why do we stop at the first order of expansion of the action to get the Euler-lagrange equations and it turns out they exactly get us the Newtonian equations. ...
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### Parity tranformation on Lagrangian of free fields

Free lagrangians of scalar, Dirac field and vector fields are always invariant under Parity. I am able to get this result mathematically, but I want to know if there is any obvious reason for it. ...
The Euler-Lagrange equation is about the functional $$\int_{t_1}^{t_2} L(q, \dot{q}, t ) dt .$$ From a mathematical point of view, a simpler functional might be $$\int_{t_1}^{t_2} L(q, t ) ... 1answer 79 views ### Derivation in Modern Supersymmetry by Terning I am trying to do some calculations from Modern Supersymmetry by Terning and I am stuck on how he derived a particular term. Specifically, I am looking at 2.67 on page 27. My current work is below.$$...
The electron and neutrino can interact through an intermediary Z boson, via the Lagrangian:  L= \frac{1}{2} \partial_\mu \phi_Z \partial^\mu \phi_Z - \frac{1}{2} m_Z ^2 \phi_Z ^2 -g_{\nu} \phi_Z \...