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 ...
281 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 ...