Joy, Fred, ++: Re this equation in Joy, Peres, Dirac?
Posted:
Tue Apr 04, 2017 1:50 pmby Xray
I'm interested in understanding the following equation and its variants in detail:
(iσ·a)(iσ·b) = −a·b1 − iσ·(a×b). (1)
(1) is used by Joy.
Peres' text book -- Quantum Mechanics (1995), page 162 -- has a variation.
I suspect there's one in Dirac's textbook too? And Geometric Algebra too?
Questions:
1. What is the best name (and what are other names) for this equation?
2. Where can I find it developed/derived online? Especially under GA?
3. Is σ in (1) Pauli's vector of matrices?
4. Any other hints for a beginner tackling this subject?
Thanks
Re: Joy, Fred, ++: Re this equation in Joy, Peres, Dirac?
Posted:
Tue Apr 04, 2017 4:27 pmby FrediFizzx
Xray wrote:I'm interested in understanding the following equation and its variants in detail:
(iσ·a)(iσ·b) = −a·b1 − iσ·(a×b). (1)
(1) is used by Joy.
Peres' text book -- Quantum Mechanics (1995), page 162 -- has a variation.
I suspect there's one in Dirac's textbook too? And Geometric Algebra too?
Questions:
1. What is the best name (and what are other names) for this equation?
2. Where can I find it developed/derived online? Especially under GA?
3. Is σ in (1) Pauli's vector of matrices?
4. Any other hints for a beginner tackling this subject?
I don't think there is a particular name; it is just a mathematical identity involving the Pauli spin matrices. Just do the math on the LHS of the equation.
https://en.wikipedia.org/wiki/Pauli_mat ... ss_product.
Re: Joy, Fred, ++: Re this equation in Joy, Peres, Dirac?
Posted:
Tue Apr 04, 2017 7:08 pmby Xray
Thanks Fred, lovely reference!
I thought it was called "Dirac's relation" -- and I'm keen to name it correctly IF that is its original name (which I suspect it is). However -- in that there is NOW at least one other "Dirac relation" -- I'll work with "Dirac's spin relation".
Re: Joy, Fred, ++: Re this equation in Joy, Peres, Dirac?
Posted:
Tue Apr 04, 2017 7:17 pmby Joy Christian
Xray wrote:Thanks Fred, lovely reference!
I thought it was called "Dirac's relation" -- and I'm keen to name it correctly IF that is its original name (which I suspect it is). However -- in that there is NOW at least one other "Dirac relation" -- I'll work with "Dirac's spin relation".
It is called Pauli identity.
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