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Phillip Helbig---remove CLOTHES to reply
#4
Oct12-06, 04:42 AM
P: n/a

Hi, I've been trying to 'get' spinors, and . . . .


In article <1127087775.061608.65650@g43g2000cwa.googlegroups.com>, "Dom"
<Dom_isnt@yahoo.co.uk> writes:

> I've been trying to 'get' spinors, and I would appreciate a little help
> with a question on chirality.
>
> In two dimensions the two component spinor is mapped onto the vector
> space via the Pauli matrices sigma_1 and sigma_2. Eg x = psi^{dagger}
> sigma_1 psi. The chirality operator is C = -i*sigma_1*sigma_2 =
> sigma_3. The an arbitrary spinor may be projected into its left and
> right handed Weyl spinors using (1[+/-]P)psi. However what I do not
> understand, is that a purely left handed or right handed spinor have
> only the vector 0 associated with them, using the above mapping. Can
> someone shed some light on this please.


Have you had a look at Penrose's "The Road to Reality"? There is a lot
on spinors in the book, and he provides a lot of background material.
In any case, the stuff on spinors has lots of useful references.

Let me recommend this book in general. While of course it cannot cover
everything (and doesn't try to), I think it is a good survey of the
mathematical aspects of many important areas of physics. (About half
the book is just maths, a prerequisite for the rest.) Penrose also
points out where his own minority views are not part of mainstream
thought, so there is no danger of getting a false impression of what
mainstream thought is. Despite its size, though, it does not contain
all of Penrose's other semipopular books, nor is it a "best of Roger".
It actually stands on its own, and the overlap with his other popular
books is not that large.