Linked Questions

8
votes
3answers
6k views

Physical meaning of the Lagrangian function [duplicate]

In Lagrangian mechanics, the function $L=T-V$, called Lagrangian, is introduced, where $T$ is the kinetic energy and $V$ the potential one. I was wondering: is there any reason for this quantity to be ...
1
vote
0answers
110 views

What is the physical significance of a Lagrangian and an action in particle physics? [duplicate]

I’m currently studying for a particle physics module about the standard model and there is a lot of material on Lagrangians (curly L) and actions (S). I’m not quite sure what both of these quantities ...
0
votes
1answer
87 views

Information contained in Lagrangians and actions [duplicate]

I've been looking into analytical mechanics with the intention of finding out more about Lagrangians and actions. As far as I currently understand it, the Lagrangian is formed with positions and ...
67
votes
14answers
8k views

Lagrangians not of the form $T-U$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are ...
36
votes
4answers
16k views

The meaning of action

The action $$S=\int L \;\mathrm{d}t$$ is an important physical quantity. But can it be understood more intuitively? The Hamiltonian corresponds to the energy, whereas the action has dimension of ...
25
votes
2answers
11k views

Why on-shell vs. off-shell matters?

The definitions between on- and off-shell are given in Wikipedia. Why is it so important in QFT to distinguish these two notions?
11
votes
3answers
4k views

Hamilton-Jacobi Equation

In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
9
votes
3answers
3k views

Meaning of kinetic part in the Lagrangian density?

What is the physical meaning of the kinetic term in the classical scalar field Lagrangian $$\mathcal{L}_{kin}~=~\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi)~?$$ It gives how does the field change ...
7
votes
1answer
5k views

Hamilton's characteristic and principal functions and separability

Just hoping for some clarity regarding Hamilton's characteristic function $W$. When we take a time independent Hamiltonian we can separate the Principal function $S$ up into the characteristic ...
0
votes
1answer
699 views

Why the Lagrangian $L$ is KE - PE? Why not KE + PE!

With Lagrangian, is there any way to intuitively grasp why total energy equals the difference between the kinetic and potential energy? Seems counter-intuitive - whereas Hamiltonian calculation (sum ...
5
votes
2answers
474 views

What exactly is the Action? (Learning lagrangian)

I have been trying to wrap my head around lagrangian mechanics but I find some parts confusing. For example, what exactly is action and why is it defined by the Kinetic energy minus the potential ...
8
votes
1answer
393 views

Heuristic Motivation for Lagrangian Formalism

Does anyone know a good heuristic motivation for the Lagrangian Formalism? I think most physicist just accept at one point that it works and thats that. I think I understand the historic origin. ...
5
votes
1answer
469 views

Derivation of Noether's theorem - A problem with physical significance

My question is about the field theoretic version of Noether's theorem. I am deeply troubled by one of the hypotheses of the theorem. As it is the standard textbook for Lagrange mechanics, I'll follow ...
6
votes
1answer
219 views

Uses for Action from Lagrangian Mechanics

In my course on Lagrangian/Hamiltonian mechanics I noticed that we dealt with finding the stationary point of the change in action $ \delta S $ and we were never really doing anything with $ S $ ...
5
votes
1answer
209 views

In what sense (if any) is Action a physical observable?

Is there any sense in which we can consider Action a physical observable? What would experiments measuring it even look like? I am interested in answers both in classical and quantum mechanics. I ...

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