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some thoughts on \nabla, Laplace and Quabla

Here are some thoughts on \nabla and the Laplace and d'Alembert
operators needed in theoretical physics. I don't know if there are
plans to include specific glyphs for the Laplace and d'Alembert
operators that are missing in the present cm fonts. If there are,
you can probably ignore the rest, if not, please read on and do
something about them ...

* \nabla and the Laplace operator

I recently had a private discussion with J\"org Knappen concerning
the apperarence of \nabla and the Laplace and d'Alembert operators
in theoretical physics. Although there are no specific recommendations
in the IUPAP standard (IUPAP = Intl. Union of Pure and Appl. Phys.),
we seemingly both agree that \nabla and the Laplace operator should
be visually compatible.

While there is a perfectly suitable \nabla symbol in the present
cmsy, there is *no* specific symbol for the Laplace operator. It
is usually refered to as \Delta (upright), but that's unfortunate
if uppercase greek letters (when used as identifiers) are set in
math italics instead of math roman.

I therefore suggests that we have a separate glyph reserved for the
Laplace operator, especially to avoid unwanted dependencies between
identifiers and symbols. \Laplace would be an obvious name for it,
but if anyone has a better idea, just say so.

A seperate glyph for \Laplace would also allow a type designer to
replace \nabla and \Laplace by triangles of uniform line thickness
withouth interfering with greek letters if it is desired.

* the d'Alembert (or Quabla) operator

Another symbol often needed in relativistic wave equations is the
d'Alembert operator, sometimes refered to as Quabla. It basically
looks like a square box, but the \Box from the lasy font is a bit
too small. A sepearate symbol for \quabla, that is adjusted in
size to match \nabla and \Laplace, would definitely be desirable.

(In fact, I recall that there was a specific request to include
the d'Alembert operator at the math font BOF with Norbert Schwarz
that was held at the DANTE meeting 1992 in Hamburg. I don't know
how much of the outcome has reached this working group as input.)

In any case, I regard \nabla, \Laplace and \quabla as a group of
symbols that should be dealt with together. They should match in
size (btw: Is \Laplace = \Delta actually an upside-down \nabla
or are there any differences?) and maybe also in stroke thickness
(\Box has rather thin lines compared to the others), but that's
a question of design and not of encoding. A need for these symbols
is definitely there, as everyone in theoretical physics would
probably agree. They are perhaps much more important than some
of the other symbols under consideration.

In case you have already decided to include \Laplace and \quabla
please excuse my lenghty argument, but I didn't know what the
current situation is. Please enlighten me!


Ulrik Vieth.

P.S: A note on usage: I observed that American books or papers often
use $\nabla^2$ where European papers usually use $\Delta$. I don't
know if there's any deeper reason behind it, but I guess that this
is probably the reason why there is only a \nabla in the cm fonts.
For the same reasons (American typesetting conventions) uppercase
greek letters are taken from math roman instead of math italics,
which is also different from traditional European typography. We
should try to allow more flexibility for national math typesetting
conventions this time, shouldn't we?