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 ...
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 ...
104 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. ...
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 ...
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, ...
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 ...
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 ...
23k 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 ...
897 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 ...
421 views

QFT's that have no action

What does it mean to have a QFT that can not be encoded by an action. What is by far the most powerful approach of study in such a case. What is the best studied physical theory that falls into this ...
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. ...
970 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 ...
2k views

Is there a valid Lagrangian formulation for all classical systems?

Can one use the Lagrangian formalism for all classical systems, i.e. systems with a set of trajectories $\vec{x}_i(t)$ describing paths? On the wikipedia page of Lagrangian mechanics, there is an ...
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 ...
287 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 ...
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 ...
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 ...
280 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 ...
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 ...
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 ...
95 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 ...
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 ...