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Pauli matrices and the Levi-Civita tensor : commutation relations

  • Thread starter Dixanadu
  • Start date
  • #1
254
2

Homework Statement


Whats up guys!

I've got this question typed up in Word cos I reckon its faster:
http://imageshack.com/a/img5/2286/br30.jpg [Broken]

Homework Equations



I don't know of any

The Attempt at a Solution


I dont know where to start!!! can u guys help me out please?

Thanks!
 
Last edited by a moderator:

Answers and Replies

  • #2
12
0
You can start by multiplying each possible combination of pauli matrices. Do that and factor out a 1 or -1, which can be replaced with a Levi-Cevita symbol. Use i = 1, j = 2, k = 3.
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618
Sure, just check it by putting the matrices into the commutation relation. For example, show ##[\sigma_1,\sigma_2]=\sigma_1 \sigma_2-\sigma_2 \sigma_1=i\sigma_3##. But it's not going work very well until you fix ##\sigma_3##. That's not a Pauli matrix.
 

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