Talk:Grassmann number

Physics Low‑importance

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Numbers

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don't understand[edit]

I don't really understand what is said about grassman numbers in physics. How can we give an interpretation of "raising operator" ? Someone can give an example whith n=2 please ? Thanks.

Who is Candlin?[edit]

He invented this--- but there is no biography on him, no details of what he is doing, or if he is still alive. He should have his own page.Likebox (talk) 20:53, 27 August 2008 (UTC)[reply]

Better remove this article[edit]

This article is full of mistakes and arbitrary opinions.

First, it was Grassmann, not Candlin, who invented Grassmann numbers, or, to be exact, the exterior multiplication. No Fermionic fields were known at that epoch, of course.

Second, D. J. Candlin, in his very ingenious paper, did some brilliant anticipation, but by no means invented Berezin integral in anticommuting variables.

So, in order that we no write here just someone's arbitrary opinions, I think a wide discussion on this subject is necessary, involving both mathematicians and physicists.

Paloff (talk) 10:32, 17 October 2009 (UTC)[reply]

Lede - doubts[edit]

I've only superficial/introductory understanding of this subject but I question several of the lede's claims.
The most questionable is the second sentence:"A collection of Grassmann variables \theta_i are independent elements of an algebra which contains the real numbers that anticommute with each other but commute with ordinary numbers x: [equations removed]." First, grade school English grammar: "A collection ... are" is simply wrong. "A collection of Grassman variables ^is...". Second, Why is the discussion of VARIABLES when the article is about NUMBERS? Third, which is it? does the COLLECTION of Grassman variables "contain" the real numbers or does the ALGEBRA? Fourth, what are "ordinary" numbers? The obvious implication is that they are different from the real numbers mentioned in the same sentence. Fifth, why aren't complex numbers included? (Note that imaginary numbers wouldn't be considered "ordinary" by 99.9% of us).
It seems to me, for what its worth, that a 'better' introduction would be way of comparing them to i (√-1). i is a useful but abstract invention having no "real physical" presence and having the 'impossible' property that i*i produces a negative number. In physics, Grassman numbers are introduced as a set of one or more 'numbers' which have the following properties:
1) Multiplying any one Grassman number θ by itself produces zero, θ×θ = 0
2) Multiplication of any two (different) Grassman numbers is anticommutative: θ_i×θ_j = -(θ_j×θ_i)
3) Multiplication of a Grassman number with any real or imaginary (or complex) number is commutative: θ × X = X × θ; θ × iX = iX × θ
The following sentence uses the term "generator" without ANY explanation. This is very unhelpful, and also unnecessary. It also seems to me that the term "algebra" is used here in a way which misleads. Also, the even-odd nature of Grassman algebras doesn't receive the emphasis is should, nor do I see ANY mention that because higher powers of θ vanish, that functions of θ are very limited (simple). Finally, I see no discussion of division by Grassman numbers, which seems important to me. Oh, and is it true that log(θ) = log(½) = -0.69315...? Does this connect Grassman numbers to √-X ? (ie log(√X) = ½×log(X))(216.96.77.81 (talk) 17:42, 9 November 2014 (UTC)[reply]

So fix it. YohanN7 (talk) 09:23, 11 November 2014 (UTC)[reply]

I fixed it in such a way that I hope it is no longer confusing. 67.198.37.16 (talk) 16:46, 28 September 2016 (UTC)[reply]

And we all thank the anonymous editor who has now beefed up the article. I changed rating to "C", but possibly it should be "B". YohanN7 (talk) 11:51, 12 July 2017 (UTC)[reply]

No, it should not yet be "B". It needs a few more references, and many more inline citations. But that burden is to be shared. I'll try to remember to add citations whenever I bump into citable material in what I read (when pursuing similar topics). YohanN7 (talk) 11:58, 12 July 2017 (UTC)[reply]