Linked Questions

5
votes
1answer
283 views

How the lagrangian density is found?

In Classical Mechanics one usually considers the Lagrangian as $L = K - U$ where $K$ is the kinetic energy of the system and $U$ is the potential energy. One then gets the Euler-Lagrange equations and ...
4
votes
1answer
146 views

Is there an action for every physical law?

Given an action, I can get the differential equation governing the evolution of the system by applying the principle of least action. Does it work the other way around? Given any differential ...
4
votes
1answer
930 views

Can we derive most fundamental laws from the Action Principle? [duplicate]

It is said in the book Fearful Symmetry - The Search for Beauty in Modern Physics that we can derive all basic laws in physics from a simple principle called Least Action Principle (although it may be ...
4
votes
1answer
453 views

When can a classical field theory be quantized?

Given a classical field theory can it be always quantized? Put in another way, Does there necessarily need to exist a particle excitation given a generic classical field theory? By generic I mean all ...
1
vote
1answer
288 views

Why do Lagrangians and Hamiltonians give the equations of motion? [duplicate]

I remember asking my second year Mechanics teacher about why do the Lagrangians give the equations of motion. His answer was that there is no answer to that, it is an empirical fact, and that asking ...
0
votes
1answer
216 views

When can I apply Lagrangian mechanics?

I am trying to understand Lagrangian mechanics. I am having trouble capturing all of the nuances in one gulp. I can see the equations, but not necessarily the semantics behind such equations. I ...
1
vote
0answers
44 views

Why do we derive more fundamental quantum theories from less fundamental classical theories? [duplicate]

In almost every derivation of a quantum theory (quantum mechanics or quantum field theory), we start with a classical theory using classical equations and quantize it (by imposing certain constraints ...
1
vote
0answers
96 views

What are the other possibilities for a Lorentz invariant interaction?

In Weinberg's QFT book, Chapter 3, he shows that if the interaction term $V(t)$ is of the form $$V(t)=\int \mathcal{H}(t,\mathbf{x})d^3\mathbf{x},$$ where the operators $\mathcal{H}(x)$ are scalars ...
1
vote
0answers
106 views

Which class of Dynamical Systems is governed by Lagrangian Dynamics? [duplicate]

Lagrangian formalism is a technique using which we can obtain the time evolution of a dynamical system. Given a dynamical system, can we say whether or not we can write down a Lagrangian (solving it ...
1
vote
0answers
54 views

Is there a method to obtain a Lagrangian from the equations of motion? [duplicate]

From the standpoint of the mathematical framework behind Lagrangians and their corresponding action, is there a method to invert the process? If not, is this an open question or is there some aspect ...
1
vote
0answers
454 views

Why does Principle for least action hold for classical fields [duplicate]

Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field $\phi(\mathbf x)$. Then then actual value of the field $\phi(\mathbf x)$ can be computed from the ...
0
votes
0answers
28 views

How general is the Lagrangian formulation? [duplicate]

Haven't seriously tackled this problem myself because it's been awhile since I've done any hard mathematics and I'm a bit rusty. However, you needn't spare the math in your answers. I've been ...
0
votes
0answers
42 views

Must there exist a Lagrangian for any 2nd order ordinary derivative equation? [duplicate]

We know if there exist a Lagrangian of some ODE, then it must exist many equivalent Lagrangian. My question: Then must there exist a Lagrangian for any 2nd order ODE? If not, do we have some ...
0
votes
0answers
102 views

Why should physical theories always have a Lagrangian formalism? [duplicate]

I've often heard that every physical theory has some kind of Lagrangian formalism, or a formalism in terms of a principle of stationary action. The Standard Model has one, General Relativity has one, ...
0
votes
0answers
55 views

Does the principle of stationary action always work? [duplicate]

Give some Lagrangian we use the principle of stationary action to find the desired euqations of motion for something (e.g. a field). A lot of modern physics seems to be based on the principle of ...

15 30 50 per page