# Tag Info

1 vote

• 160

• 62.8k

### Four-divergence term in Lagrangian

It is known that adding a four divergence term, $\partial_\mu A^\mu$ does not affect the equations of motion. I am trying to reason this based on the Euler-Lagrange equation. But I want to show this ...
• 20k
Accepted

### How can a scalar field have components and how do I interpret these components?

The components of the electric (field) vector $\vec{E} \,$ "live" in ordinary three-dimensional space (where we also live in). If you place a small test charge $q$ at some point in space (...
• 6,018
1 vote

### Oscillating inverted hemisphere Lagrangian mechanics problem

In any circumstance, we can account for the kinetic energy of a rotating object in one of two ways: $T = \frac12 I \omega^2$, where $I$ is the moment of inertia about the (instantaneous) pivot point ...
• 48.9k

### Oscillating inverted hemisphere Lagrangian mechanics problem

By considering a rolling full sphere (or a wheel for simplicty), its clear, that the full sphere center moves horizontally like an the axis of a wheel during oscillating by rolling without slip. The ...
1 vote

### Oscillating inverted hemisphere Lagrangian mechanics problem

Probably simplest to take the moment of inertia about the hemisphere's centre of mass. Then if the centre of mass moves the hemisphere has translational kinetic energy and if the hemisphere rotates ...
• 53.1k

### Equations of motion for Lagrangian of scalar QED

I have to determine the equations of motion for both the complex scalar field $\varphi$ and the electromagnetic field $A_\mu$ by using the Euler-Lagrange equations. Now I know, that because the ...
• 20k
1 vote

### What is the physical meaning of the counterterms we add in Lagrangians?

There are two answers to this depending on what you mean. Based on your question it seems both levels of understanding would be useful. The second answer actually has more of a "physical meaning&...
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### Onsager-Machlup functional and the Boltzmann distribution

One can find the extremum trajectory and the quadratic fluctuations around it - by usual procedure of varying action. (If I am not mistaken, this leads directly to Newton equations with damping.) This ...
• 58.7k

• 53.1k
Accepted

### Why are 2-point functions Green's functions?

It follows from the Schwinger-Dyson equations. Let's prove it for the case you're interested in (though the equations are more general). I will do it for a scalar field and let you work out the ...
• 26k
1 vote
Accepted

### Problem solving for Wilsonian Effective Action

I haven't checked the details of your integrals, but assuming that that's all done correctly, the only thing you're missing is log rules and a series expansion. Using $a_i$ to mean the corresponding ...
• 740
Accepted

• 16.4k

### Derivation of the geodesic equation. Why do we start with the special relativistic action?

The derivative $\frac{ds}{d\lambda}$ gives a vector field which is tangent to the world line at every point of the world line. This tangent vector does not depend on how space behaves away from the ...
• 463