The Naked Spinor and related stuff

[RiccardoVen]

Hello,
studying deeply the Dirac equation in its different aspects, I came across the series of book
"The Naked Spinor", and all their related sibliings, made by Dennis Morris.
It's a quite new series of book, which states how current physics in ALL its aspects could be easily made born from a spinor math under the wood. In particular, in its: "Upon General Relativity: How GR Emerges from the Spinor Algebras" it demonstrates how we could derive ALL assumptions made by GR (like 3+1 spacetime) from a very simple spinor algebra.
I was wondering whether this approach is related to spin networks and/or the Penrose view of GR based on Spinors.
This is really cool to me, but I'm trying to understand if this is a single separate reasearch made by one man band, or it's a new branch of Physics which is gaining rapidly its popularity (as Morris is saying in its books).
If I posted this in the wrong place, I apologize and please move it wherever you fell it correct.

Thanks

 

[robphy]

Hello,
studying deeply the Dirac equation in its different aspects, I came across the series of book
"The Naked Spinor", and all their related sibliings, made by Dennis Morris.
It's a quite new series of book, which states how current physics in ALL its aspects could be easily made born from a spinor math under the wood. In particular, in its: "Upon General Relativity: How GR Emerges from the Spinor Algebras" it demonstrates how we could derive ALL assumptions made by GR (like 3+1 spacetime) from a very simple spinor algebra.
I was wondering whether this approach is related to spin networks and/or the Penrose view of GR based on Spinors.
This is really cool to me, but I'm trying to understand if this is a single separate reasearch made by one man band, or it's a new branch of Physics which is gaining rapidly its popularity (as Morris is saying in its books).
If I posted this in the wrong place, I apologize and please move it wherever you fell it correct.

Thanks

I haven't seen this book by Dennis Morris... but I have peeked into another one of his books... I think the one on Complex Numbers.
I recall that the Complex Number book had a lot of formulas illuminating some special cases that are probably of more interest to algebraists rather than physicists. I don't think a typical physicist would gain anything from that Complex Number book.
It seems (from reading the Amazon description) that the Naked Spinor is about Clifford Algebras (of which spinors and tensors are special cases).

David Hestenes has been an advocate of using Clifford Algebras in physics...and there are numerous monographs trying to illuminate its utility in physics.
Although Clifford Algebras are interesting... I am personally not yet fully sold on it as tool to understand relativity or other branches of physics.
(Certainly some aspect of Clifford Algebras are needed for the gamma matrices.)
I acknowledge that there is this structure and formalism...
but I'm not yet ready to invest the time in it
since I am unsure if the output is worth my input.

My feeling (based on my experience with the Complex Numbers book)
is that I don't have high hopes that it'll be that enlightening... but I'd be willing to peek into it.

My $0.02.

 

[RiccardoVen]

Thanks for your answer Robphy, it's highly appreciated.
I know what book you are talking about, i.e.:

Complex Numbers the Higher Dimensional Forms: Spinor Algebra

At the very begin of The Naked Spinor book, the author suggests two books to be read
as introduction to it, i.e.:

1) The Physics of Empty Space

and

2) Complex Numbers the Higher Dimensional Forms: Spinor Algebra

The first is about generic rotations (also non commutative ones), while the second puts the basis
for a different view of Clifford algebra (as the author describes it). I have a good knowledge of groups,
and a good basis about algebra (more oriented to elliptic curves, LFT etc etc), but nevertheless I have troubles
in following smoothly The Naked Spinor book. My road would be to understand better the Penrose books
about spinors and twistors, since I'm really interested in rewiring myself to a spinor-based GR.
This is achieved by another books of the author, i.e.:

http://www.ebay.it/itm/311512861706?_trksid=p2060353.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT

I've followed that book for some chapters without problems, since I have some basis on GR, but then it started
referring to concepts contained in the above mentioned basis books.
So I decided to buy them to have a better foundation on its theory, eventually.

I'm following a parallel route as well, studying QFT and, prior to it, RQM leading to Dirac's equation.

So, my real point is to REALLY understand how spinors from Dirac's equation are coming out as a vector of complex numbers.
That is, I'd really want to understand have a better grasp between the Dirac's equation and the spinors, leading
to Clifford's Algebra.
To achieve this, I've also bought a book, suggested by the author, i.e.:

Clifford Algebras and Spinors
Lounesto, Pertti

I hope all those books may help me in having a better grasp on Penrose & Rindlers book.

I'm also in Theller's book about The Dirac Equation (I already own both his books about Visual QM
and I find them very effective), but I don't know if this will help in understanding better spinors
from a group theory point of view.

Thanks for your help.

 

[cratylus]

I started reading Hladik's "Spinors in Physics" , which is quite good, I think.

 

[member 11137]

Hello,
studying deeply the Dirac equation in its different aspects, I came across the series of book
"The Naked Spinor", and all their related sibliings, made by Dennis Morris.
It's a quite new series of book, which states how current physics in ALL its aspects could be easily made born from a spinor math under the wood. In particular, in its: "Upon General Relativity: How GR Emerges from the Spinor Algebras" it demonstrates how we could derive ALL assumptions made by GR (like 3+1 spacetime) from a very simple spinor algebra.
I was wondering whether this approach is related to spin networks and/or the Penrose view of GR based on Spinors.
This is really cool to me, but I'm trying to understand if this is a single separate reasearch made by one man band, or it's a new branch of Physics which is gaining rapidly its popularity (as Morris is saying in its books).
If I posted this in the wrong place, I apologize and please move it wherever you fell it correct.

Thanks

Just a suggestion which should make you perhaps happy in your quest: look (under your own responsability*) at "https://archive.org/details/TheTheoryOfSpinors" and read E. Cartan's book on the topic. You will discover a progressive introduction to the concept of spinor and somewhere in the book, discover the logical link with Clifford's algebra. The Dirac's equation is introduced at the end of the book. Good luck.

*Important abstract of the "Terms of Use, 31 Dec 2014

This terms of use agreement (the "Agreement") governs your use of the collection of Web pages and other digital content (the "Collections") available through the Internet Archive (the "Archive"). When accessing an archived page, you will be presented with the terms of use agreement. If you do not agree to these terms, please do not use the Archive’s Collections or its Web site (the "Site").

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[RiccardoVen]

Access to the Archive’s Collections is provided at no cost to you and is granted for scholarship and research purposes only...".

Sorry I just noticed now I got still an unread reply to my post. Actually I've already a solid copy of the book, so I can access it directly without the web.
However, this book is a bit too technical to me, and I'm waiting to get a bit more understanding about spinors before digging in it.

Actually I'm facing spinors to reach their high level parents, the twistors. I've always been fascinated by them, since I started reading the two
Penrose pillars book on the topic (again, they are a bit too advanced to me).

I know, after many years, the twistor are (or were few years ago) gaining a new season thank to Witten and Nima use of them in string theory.
Also the LQG is quite connected to them, so I'd like to have a grasp on them (more than a grasp, actually :-)).

Of course I'd need to have a good knowledge on spinors, first. Actually I'm looking to a more geometrical picture of them, not so
focusing on their algebra only. The Lounesto book is good, by it's more oriented to the algebra POV.

 

[member 11137]

Sorry I just noticed now I got still an unread reply to my post. Actually I've already a solid copy of the book, so I can access it directly without the web.
However, this book is a bit too technical to me, and I'm waiting to get a bit more understanding about spinors before digging in it.

Actually I'm facing spinors to reach their high level parents, the twistors. I've always been fascinated by them, since I started reading the two
Penrose pillars book on the topic (again, they are a bit too advanced to me).

I know, after many years, the twistor are (or were few years ago) gaining a new season thank to Witten and Nima use of them in string theory.
Also the LQG is quite connected to them, so I'd like to have a grasp on them (more than a grasp, actually :-)).

Of course I'd need to have a good knowledge on spinors, first. Actually I'm looking to a more geometrical picture of them, not so
focusing on their algebra only. The Lounesto book is good, by it's more oriented to the algebra POV.

Thanks for your reply. The reason why I proposed Cartan's book lies on the fact that that book is a sort of historical reference. He was the initiator for that (at the beginning of the 20th century) new concept. The book is a translation of lectures he gave and in which the concept is slowly emerging. I am myself no professional and just studying all this for fun (intellectual curiosity and mental challenge with no hope to gain any feedback - I am no more the youngest!). Clifford's algebra appears in the book... I would say by the way. Representing spinors is not so easy. A spontaneous answer is relating them sometimes to rotations. But I am quite sure that that type of representation is totally incomplete. Since I am myself more working at a relatively high abstract level... and don't need so much concrete representations... this lack of connection with the reality is not a problem. Anyway, thanks again.

 

[cratylus]

I'm struggling towards a geometric understanding myself, but isn't the key idea to imagine a triad ( frame/ corner ) and then encode infinitesimal movements of the frame - Hladik does this with two 3 vectors with same length and origin( the image of a segment of a rotation ) and then forms a single complex vector by multiplying the target vector by i