# What's that symbol?

1. Mar 2, 2005

### TheDestroyer

What's that symbol????

Today we've studied in the electrodynamique an affector named dalamperes affector defined as:

$$\nabla^2 - \frac{1}{c^2}\cdot\frac{\partial^2}{\partial t^2}$$

c is the speed of light in vacuum, t is time, $$\nabla$$ is hameltons affector,

HERE IS THE QUESTION:

What's the name of the symbol used in that affector, the symbol is like a square and has the second degree, and does it have a definition for the first degree? and what is it? can some one explain everything about it?

2. Mar 2, 2005

### dextercioby

God,u mean the d'Alembertian,a.k.a.BOX...
Defined in SR as:
$$\Box =:\partial^{\mu}\partial_{\mu}$$
,its form depends on the metric chosen...In your case the metric is:
$$\eta_{\mu\nu}=diag \ (+,+,+,-)$$ (rather uncharacteristic)

Nabla is no longer called Hamilton's...It's called simply nabla.

Daniel.

Last edited: Mar 2, 2005
3. Mar 2, 2005

### TheDestroyer

Dextercioboy thank you for the specific answer, but i didn't understand:

1- What's the name of that symbol, is it aka box????
2- Does it have a first degree definition?
3- and what's the meaning of what's after Eta symbol you've written above?

Please try being more simple and specific with me, The language is causing me to not understand

4. Mar 2, 2005

### dextercioby

D'ALEMBERT-IAN after the french mathematician Jean Le Rond d'Alembert,the one which discovered the waves' equation...

No.It's a second order linear differential operator...

You mean "diag"...?It's a shorthand notation for "diagonal".It means the matrix $$\hat{\eta}$$ is diagonal...

On normal basis i should have written it:
$$(\hat{\eta})_{\mu\nu}=\left(\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&-1\end{array}\right)$$

Daniel.

Last edited: Mar 2, 2005
5. Mar 2, 2005

### TheDestroyer

Oh my god, calm down, why you're getting nervous so quickly,

...........

................................

It's better for me to not understand, thanks

6. Mar 2, 2005

### dextercioby

Who said i wasn't calm...?I took it as u didn't see the name very clearly & that's why i wrote it bigger,nothing else...

Daniel.

7. Mar 2, 2005

### TheDestroyer

Thank you anyway dextercioboy, you're a genius in maths and physics and that doesn't help you to teach a university boy like me, i'll try finding the solution in our library and internet,

8. Mar 2, 2005

### HallsofIvy

Staff Emeritus
??? He answered precisely your question : the symbol you asked about is called, informally, "box", similar to "del" for the upside down triangle symbol, and, more formally, the "D'Alembertian". It is an extension of the LaPlacian: where the LaPlacian, in 3 dim space, is the sum of the second derivatives wrt each coordinate, the D'Alembertian includes subtracting the second derivative wrt time.

"box" f= $\frac{\partial^2 f}{/partial x^2}+ \frac{\partial^2f}{/partial y^2}+ \frac{\partial^2 f}{/partial z}- \frac{\partial^2f}{/partial t^2}$

Last edited: Mar 2, 2005