Skip to main content

New answers tagged

0 votes

Is Electrostatics Local?

Is Electrostatics Local? No, electrostatics is a non-local theory. This is clear from, say, the interaction term: $$ V_{non\;local} = \int d^3 r \rho(\vec r)\phi(\vec r) = \int d^3r d^3r' \rho(\vec r)...
hft's user avatar
  • 21.1k
0 votes

Is Electrostatics Local?

The electrostatic potential is always a little funny because of the gauge freedom to add any constant. It is somewhat "nonlocal" in the sense that the equation $\nabla^2 \phi = -\rho$ must ...
tparker's user avatar
  • 48.1k
0 votes
Accepted

Classical open string in Polchinski -- consistency of Neumann boundary conditions with gauge choice

Let's use a trivial generalization of what you wrote which is \begin{align} \partial_\sigma X^\mu = 0 \; \text{at} \; \sigma = 0,l \Rightarrow h_{\sigma b} = 0 \; \text{at} \; \sigma = 0,l. \end{align}...
Connor Behan's user avatar
  • 8,032
2 votes

Variation of the Lagrangian expressed as a time derivative of a function

To build intuition, you can consider a 1D particle in a uniform force field (eg free fall) with the Lagrangian: $$ L=\frac12\dot x^2-x $$ and equation of motion: $$ \ddot x+1=0 $$ The system is ...
LPZ's user avatar
  • 12.8k
2 votes
Accepted

Variation of the Lagrangian expressed as a time derivative of a function

OP already seems aware that Ref. 1 on p. 102 implicitly is talking about 2 different types of (infinitesimal) variations: i. Ordinary variations to derive EL equations. These do satisfy boundary ...
Qmechanic's user avatar
  • 205k
1 vote

Can we glue the Schwarzschild and the de Sitter metrics at their event horizon?

Yes, it is possible. What you need are the so-called junction conditions, which to my knowledge were originally derived by Israel. They are reviewed in some standard books in general relativity, such ...
Níckolas Alves's user avatar
1 vote

Eigenstates of the Laplacian and boundary conditions

If we use Dirichlet ($f(x)= 0$ if $x$ is on the box's boundary) or von Neumann ($\nabla f$ is orthogonal to the normal vector of the boundary) boundary conditions , then only some linear combination ...
SolubleFish's user avatar
  • 5,944

Top 50 recent answers are included