Spinor Decomposition of a tensor

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Discussion Overview

The discussion revolves around the decomposition of a second rank tensor into components associated with different spins, specifically spin-2, spin-1, and spin-0 parts. Participants explore references and foundational concepts related to this topic, including group theory and spinors, within the context of quantum field theory (QFT).

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Nikhil inquires about the decomposition of a second rank tensor into its spin components and seeks references for further study.
  • Daniel suggests that knowledge of group theory, particularly Lie groups and their representations, is essential for tackling such problems in QFT and recommends specific group theory books and a primer by P. Ramond.
  • A later reply proposes a reference for learning more about spinors, specifically "The Theory of Spinors" by Elie Cartan.

Areas of Agreement / Disagreement

Participants provide various references and suggest foundational knowledge, but there is no consensus on a single approach or reference for the decomposition of tensors.

Contextual Notes

The discussion does not clarify the specific mathematical steps involved in the decomposition or the assumptions underlying the proposed references.

njoshi3
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Hi,

I have heard, that a second rank tensor can always be decompose into a spin-2, a spin-1 and spin-0 part, being reducible. I want to pursue this further. Can anyone suggest me a nice reference for it?

TIA

Nikhil
 
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You have to know a little bit about group theory,namely Lie groups and their representations...Then u can attack this sort of problems emerging in QFT.

So my advice is:any group theory books which covers SU(2),SO(3)...and then try the first chapter from P.Ramond :"Field Theory:A Modern Primer"...

Daniel.
 
Thanks

Hi,

Thanks
 
Hi, my answer comes a little bit late but I would propose the following reference if you want to learn more about spinors: "The Theory of spinors" (Elie Cartan) -e.g.: Dover Books- ISBN 0-486-64070-1 / Blackforest
 

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