- #1

RiccardoVen

- 118

- 2

Hi,

some years ago when I was studying Nuclear engineering in Turin ( Italy ), I attended

some courses with prof. Tullio Regge about groups theory, spinors and twistors.

I was too young to fully understand what he was telling us, but now, after some years

of private study about Einstein's gravity and a differential geometry, I gifted myself for

my birthday with a copy of both volumes of Spinors and Space-Time.

This is, of course, really different to the normal "tensorial" approach I was used to and I'm really

fascinated by this topic. Attending some extra courses in particle physics, I saw how spinors born

to life naturally in Dirac's theory, but I wasn't aware they could be used successfully in Einstein's gravity as well.

I've read the spinors approach is handier for describing some massless phenomena, and for other the tensor approach is more appropriate.

The real interest to me is how complex numbers theory comes in help in physics here and there.

Usually, when you are able to switch some theory rearranging it under the complex line of sight, you add to it some more physics content, and I'm curious about that.

So the question is: from your experience, does spinors/twistors Penrose's approach worth the pain to break my head on it? Or it just remain actually, after 40 years, a sterile theory, which destiny is to remain in the maths tool games?

Indeed, the first volume would worth the pain even only for its interpretation of Lorentz transformation as complex Mobius transformation. This connection is really, really interesting to me.

I know recently ( where recently I meant 10 years ago ) Ed Witten has given new life to it, encompassing it somehow in string theory, but the math is too advanced to me for now( I'm studying algebraic topology and knots theory for it, but it takes a long time to master it, as you may know ).

Thanks, regards

Ricky

EDIT: I'd like to stress my point here: since I'm a physics enthusiast any theory is actually fascinating me a lot,

twistors included, and I'm constantly wondering every day about its beauty. But my time is limited and I'm putting my efforts from since last year to have a better grasp on Einstein's gravity and differential geometry, mainly doing exercises or so. This is of course really time consuming and I'd avoid to jump into "exotic" theories before having a better grasp on the main ones. Nevertheless, from my experience about complex number theory, I'd bet this should open a new insight to me ( like Riemann sphere, which impressed me so much at the very first sight), just, for instance, about the "new" induced (2,2) metric signature from it.

some years ago when I was studying Nuclear engineering in Turin ( Italy ), I attended

some courses with prof. Tullio Regge about groups theory, spinors and twistors.

I was too young to fully understand what he was telling us, but now, after some years

of private study about Einstein's gravity and a differential geometry, I gifted myself for

my birthday with a copy of both volumes of Spinors and Space-Time.

This is, of course, really different to the normal "tensorial" approach I was used to and I'm really

fascinated by this topic. Attending some extra courses in particle physics, I saw how spinors born

to life naturally in Dirac's theory, but I wasn't aware they could be used successfully in Einstein's gravity as well.

I've read the spinors approach is handier for describing some massless phenomena, and for other the tensor approach is more appropriate.

The real interest to me is how complex numbers theory comes in help in physics here and there.

Usually, when you are able to switch some theory rearranging it under the complex line of sight, you add to it some more physics content, and I'm curious about that.

So the question is: from your experience, does spinors/twistors Penrose's approach worth the pain to break my head on it? Or it just remain actually, after 40 years, a sterile theory, which destiny is to remain in the maths tool games?

Indeed, the first volume would worth the pain even only for its interpretation of Lorentz transformation as complex Mobius transformation. This connection is really, really interesting to me.

I know recently ( where recently I meant 10 years ago ) Ed Witten has given new life to it, encompassing it somehow in string theory, but the math is too advanced to me for now( I'm studying algebraic topology and knots theory for it, but it takes a long time to master it, as you may know ).

Thanks, regards

Ricky

EDIT: I'd like to stress my point here: since I'm a physics enthusiast any theory is actually fascinating me a lot,

twistors included, and I'm constantly wondering every day about its beauty. But my time is limited and I'm putting my efforts from since last year to have a better grasp on Einstein's gravity and differential geometry, mainly doing exercises or so. This is of course really time consuming and I'd avoid to jump into "exotic" theories before having a better grasp on the main ones. Nevertheless, from my experience about complex number theory, I'd bet this should open a new insight to me ( like Riemann sphere, which impressed me so much at the very first sight), just, for instance, about the "new" induced (2,2) metric signature from it.

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