The point was, I wanted to have a physical interpretation of the Lagrangian, and leave the action and the principle as abstract constructions done for who knows what reason, probably because the principle …

Lagrangian mechanics are better when there are lots of constraints. The more the constraints, the simpler the Lagrangian equations, but the more complex the Newtonian become. Lagrangian …

Is it possible to work with the real Lagrangian density and somehow get the correct commutation relations? I would have expected two Lagrangians differing by total derivative terms to give identical …

If the equation of motion comes from a lagrangian, and the lagrangian has a continuous symmetry, then Noether's theorem guarantees you a conserved current.

Jul 31, 2024 · In reading the first chapter of Mechanics by Landau and Lifshitz, there is one point on which I consistently get stuck. This regards the proof in $\\S 7$ that space homogeneity implies …

Jan 31, 2021 · In Lagrangian mechanics, you must require the coordinate system to correspond to some inertial frame of reference. After that, you can still use the typical transformations to a non-inertial …

May 2, 2020 · The definition of a symmetry of a theory is quite clear at the level of a Lagrangian. We say a Lagrangian $\mathcal {L} (\phi,\partial_\mu \phi)$ is symmetric under the transformation $\phi …

And by defining the phrase "gauge invariance of a Lagrangian" to mean that it changes to something that differs by a total derivative, then we can say the Lagrangian is gauge invariant (even though it …

Mar 21, 2021 · The third definition is different. Of course it is also related in the sense that in Lagrangian formulations of dynamics or variational problems, Lagrange multiplier methods often appear. But this …

Dec 6, 2013 · The Lagrangian, Hamiltonian formalism (with the min action principle ) represent a minimal mathematical framework that can explain a lot of experimental data, from all domains of …