Re: [Phys-l] math notation question

[John Denker <jsd@av8n.com>]

On 12/08/2006 05:58 PM, Larry Smith wrote:
> How widespread is the use of \Delta instead of \nabla^2 to mean the
> Laplacian operator in 3-D?

It's not super-widespread, but it's not super-rare, either.


> In 4-D Minkowski space the Laplacian becomes the d'Alembertian.  Should the
> d'Alembertian operator be a square with or without a superscript 2?  I've
> seen it both ways.

1) Yes, I've seen the \box^2 form ...  but AFAICT I haven't seen it in
 anything published in the last 20 years.
2) The \box form is not super-rare.
3) I've seen the \Delta form used in four dimensions at least as often as
 the \box form.
4) The \nabla^2 form works fine in four dimensions, and AFAICT is as common
 as anything else.

======================

My opinions and recommendations:

a) When writing a paper, or writing in my notebooks, I use \nabla^2 in
 all cases, in two, three, four, or however-many dimensions.

 I see no reason to change symbology when switching from three dimensions
 to four.  IMHO if you do things right, the same concepts and the same
 symbology should work just fine in all dimensions from two on up.  This
 is a sufficient reason for deprecating the \box form of the d'Alembertian.

 The \Delta form of the Laplacian and/or d'Alembertian is IMHO harmless,
 but not worth the trouble of introducing it.  It strikes me as quaint,
 like old alchemical terminology.

b) When reviewing a paper, if the authors want to use \box or \Delta,
 that's tolerable, but I would insist that they define the notation, rather
 than assuming that readers would be familiar with such things.

c) In class, I would mention the \box and \Delta notations, but I
 would not encourage them or make a big fuss over them.

d) I think \box^2 can be buried in unhallowed ground and forgotten.