Pauli's spin matrices in higher order

In summary, the conversation discusses the rules for writing Pauli's spin matrices in higher-order matrices, specifically in 4x4 matrices. It is mentioned that when dealing with s=3/2, the Pauli matrices can no longer be used as they represent s=1/2. The conversation also mentions constructing representations of the Clifford algebra using direct products of Pauli matrices, and the question of whether Pauli's 2x2 matrices for spin 1/2 can be expressed in higher-order matrices such as 3x3 or 4x4. A textbook reference or background information is requested for clarification.
  • #1
pallab
36
3
What are the rules to write Pauli's spin matrices in higher-order matrices (especially in 4x4 matrices)
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

Related to Pauli's spin matrices in higher order

1. What are Pauli's spin matrices in higher order?

Pauli's spin matrices in higher order are a set of mathematical tools used to describe the spin properties of particles in quantum mechanics. They are represented by 2x2 matrices and were first introduced by physicist Wolfgang Pauli.

2. How many Pauli's spin matrices are there in higher order?

There are four Pauli's spin matrices in higher order, denoted by σx, σy, σz, and σ0. Each matrix represents a different spin state of a particle.

3. What is the significance of Pauli's spin matrices in higher order?

Pauli's spin matrices in higher order play a crucial role in quantum mechanics as they help describe the spin properties of particles and their interactions. They are also used in various calculations and equations in the field of quantum mechanics.

4. How are Pauli's spin matrices in higher order related to the Pauli exclusion principle?

Pauli's spin matrices in higher order are related to the Pauli exclusion principle as they represent the two possible spin states of a fermion (particle with half-integer spin). This principle states that no two fermions can occupy the same quantum state, which is determined by their spin properties.

5. Can Pauli's spin matrices in higher order be applied to particles with integer spin?

No, Pauli's spin matrices in higher order are only applicable to particles with half-integer spin, such as electrons, protons, and neutrons. Particles with integer spin, such as photons, do not have spin states and therefore do not require the use of these matrices.

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