Linked Questions

74
votes
10answers
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 ...
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. ...
13
votes
1answer
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 ...
9
votes
2answers
896 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 ...
7
votes
2answers
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 ...
6
votes
4answers
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 ...
6
votes
3answers
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 ...
5
votes
1answer
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. ...
5
votes
1answer
279 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
452 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 ...
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 ...
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 ...
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 ...
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 ...

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