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That's clear: the model is (signed) numbers because charge is something that can be added and subtracted, and of which there can be an excess or a deficit.

One problem is that the same words positive/negative, used in a different domain have moral implications, and rg cannot seem to separate the different domains.

The other problem is that charge is signed but not ordered, unlike signed numbers which in addition to sign have a linear order (greater than/lesser than).

So, actually, modelling charge as signed numbers is a bad thing to do.

Technically, one can say that the irreducible representations of U(1) are isomorphic to the signed integers Z, but that is incorrect. The are isomorphic to the additive group of the integers, forgetting multiplication. If you don't have multiplication you have no way to distinguish +1 and -1.

So one possible solution is to write 1 for +1 and 1 for -1, so that

1 + 1 = 2
1 + 1 = 2
1 + 1 = 0

and there is no operation of subtraction and no negative (or positive) numbers.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:54:32 AM EST
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