Pauli's spin matrices in higher order

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Discussion Overview

The discussion revolves around the construction and representation of Pauli's spin matrices in higher-order matrices, particularly focusing on 4x4 matrices. Participants explore the implications of extending these matrices beyond their traditional 2x2 form, especially in the context of different spin values.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the intent behind the inquiry, suggesting that if the discussion pertains to spin ##s=3/2##, then the Pauli matrices would not apply as they are specific to spin ##s=1/2##.
  • Another participant proposes that the original question might relate to constructing representations of the Clifford algebra using direct products of Pauli matrices, although they express uncertainty about this interpretation.
  • A participant clarifies that their interest lies in expressing Pauli's 2x2 matrices for spin 1/2 in higher-order matrices, such as 3x3 or 4x4 matrices.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the interpretation of the original question, with multiple competing views regarding the applicability of Pauli matrices to higher-order representations and the context of different spin values.

Contextual Notes

The discussion includes assumptions about the nature of spin representations and the definitions of higher-order matrices, which may not be fully articulated or agreed upon by all participants.

pallab
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What are the rules to write Pauli's spin matrices in higher-order matrices (especially in 4x4 matrices)
 
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It's not clear what you are after? Do you mean the case ##s=3/2##? Then it's not the Pauli matrices anymore of course, because they represent ##s=1/2## and thus live in another spinor space.
 
I think the TS refers to constructing representations of the Clifford algebra via direct products of Pauli matrices, but I'm not sure. Could you give a (textbook) reference or some background, Pallab?
 
the question that can we express Pauli's 2x2 matrices for spin 1/2 in higher-order matrices, say 3x3, 4x4 arose in my mind.
 

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