# Linked Questions

0answers
107 views

### Action principles and covariant equations [duplicate]

Can every physically sound differential equation, that is covariant, deterministic etc. be derived by extremising a suitable action using a suitable lagrangian, that may be arbitary. Is this a ...
3answers
4k views

### How general is the Lagrangian quantization approach to field theory?

It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
3answers
3k views

### How do I show that there exists variational/action principle for a given classical system?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
2answers
807 views

### Does a non-lagrangian field theory have a stress-energy tensor?

In classical field theory, the stress-energy tensor can be defined in terms of the variation of the action with respect to the metric field, or with respect to a frame field if spinors are involved. ...
2answers
1k views

### Can one write down a Hamiltonian in the absence of a Lagrangian?

How can I define the Hamiltonian independent of the Lagrangian? For instance, let's assume that i have a set of field equations that cannot be integrated to an action. Is there any prescription to ...
2answers
1k views

### Damped oscillator: time-reversal, time-translation and dissipation

The equation of motion of a damped oscillator $$\frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x=0$$ which is invariant under time-translation $t\rightarrow t+a$, but not under time reversal \$t\...
4answers
1k views

### Is there any physics that cannot be expressed in terms of Lagrange equations?

A lot of physics, such as classical mechanics, General Relativity, Quantum Mechanics etc can be expressed in terms of Lagrangian Mechanics and Hamiltonian Principles. But sometimes I just can't help ...
2answers
253 views

### How rigorous can conservation of energy be made?

The principle conservation of energy is often taken as an obvious fact, or law of nature. But it seems to me the definition of energy is far from obvious, or natural: http://en.wikipedia.org/wiki/...
1answer
152 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 ...
1answer
364 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 ...
0answers
57 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 ...
0answers
56 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 ...
0answers
44 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 ...