Linked Questions

26
votes
2answers
2k views

Do “typical” QFT's lack a lagrangian description?

Sometimes as a result of learning new things you realize that you are incredibly confused about something you thought you understood very well, and that perhaps your intuition needs to be revised. ...
76
votes
10answers
24k views

Why the Principle of Least Action?

I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action ...
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 ...
0
votes
0answers
29 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 ...
6
votes
1answer
106 views

Why are action principles so powerful and widely applicable? [duplicate]

I've been trying to wrap my head around Lagrangian mechanics and Lagrangians in general, and I've found it difficult. After some thinking, I believe that the issue I have is with action principles. ...
1
vote
0answers
99 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
109 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 ...
9
votes
2answers
902 views

Is the Lagrangian approach essentially a 'theory of everything'?

From learning about the Lagrangian lately it seems that that it can underlie so many phenomena that it must be the unifying concept that underpins all physics. I often hear that physicists are ...
13
votes
1answer
291 views

How do I know how many classical limits (if any) a given quantum theory is going to have?

I was reading this, where it is mentioned that some quantum theories can have no classical limit or even more than one classical limit. A possible example might be quantum spin, which doesn't have a ...
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 ...
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
3answers
196 views

Are field theories special?

Our best descriptions of the microscopic world, that satisfy many fundamental requirements (as we know them today), are field theories. Is there something fundamental about field interactions, or are ...
0
votes
1answer
221 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 ...
0
votes
0answers
103 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
56 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