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Re: dirac matrices and QFT

• To: mathgroup at smc.vnet.net
• Subject: [mg15116] Re: [mg15083] dirac matrices and QFT
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Sat, 12 Dec 1998 03:59:15 -0500
• Sender: owner-wri-mathgroup at wolfram.com

On Thu, Dec 10, 1998, Peter Jay Salzman <psalzman at landau.ucdavis.edu>
wrote:

>hello all
>
>i'd like to name matrices \sigma^{x} and \gamma^{2} (latex notation) but
>of course, Mathematica interprets the x and 2 as exponents.
>
>is there a way of using superscripts to distinguish matrices?
>
>also, any packages out there for dirac, klein gordon or quantum field
>theory? don't now what i'm looking for per se, just curious if anyone's
>written packages which might be useful in basic calculations.
>
>pete
>
>
>--
>Check out my homepage: http://landau.ucdavis.edu/psalzman/index.html
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I can only answer the first part of the question (I think). You can do
what you want in two ways. The first way (possible only in Mathematica
3.0) is to use the Notation package. First you need  to load this
package: <UtilitiesNotation
You will then see a palette that will open automatically and let you
define bjects, like matrices that can be input using subscripts in a
WYSIWIG way. Of course the underlying imput form is going to be very
complicated, but what you see will be exponents etc.

The second way works in all versions. It is  possible to re-define the
meaning of ^ (Power) so that for particular symbols sigma and x sigma^x
does not mean the sigma to the power x but something else. You simply
unprotect Power with  Unprotect[Power]

sigma^x ^= ...

The definition you entered is now associated with Power. You then
protect power with
Protect[Power]

Now whenever you enter sigma^x you will get what you want, in other
cases exponents will have their usual meaning. I can't see any
undesirable consequences of doing this right now, but in general
changing the definitions of built in functions can be risky and have
strange and unexpected consequances.

I hope some of this at least is helpful!

http://sigma.tuins.ac.jp/
http://eri2.tuins.ac.jp/



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