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Kronecker Delta

  • Thread starter Hendrick
  • Start date
  • #1
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Homework Statement


Simplify/Evaluate these expressions involving the Kronecker delta, using Einstein's summation convention:
a)[tex]\delta_{qr}[/tex][tex]\delta_{rp}[/tex][tex]\delta_{pq}[/tex]
b)[tex]\delta_{pp}[/tex][tex]\delta_{qr}[/tex][tex]\delta_{rq}[/tex]

Homework Equations


[tex]\delta_{ij}[/tex]=0 when i =/= j
[tex]\delta_{ij}[/tex]=1 when i = j


The Attempt at a Solution


a)[tex]\delta_{qr}[/tex][tex]\delta_{rp}[/tex][tex]\delta_{pq}[/tex]
=[tex]\delta_{qp}[/tex][tex]\delta_{pq}[/tex]
=[tex]\delta_{qq}[/tex] = 3 (summation over repeated q)

b)[tex]\delta_{pp}[/tex][tex]\delta_{qr}[/tex][tex]\delta_{rq}[/tex]
=[tex]\delta_{pp}[/tex][tex]\delta_{qq}[/tex]
=(3)(3)
=9
[Am I actually able to evaluate the [tex]\delta_{qr}[/tex][tex]\delta_{rq}[/tex] part before the [tex]\delta_{pp}[/tex] part, I mean you can't do that with matrices... :S]


Thank you
 

Answers and Replies

  • #2
phyzguy
Science Advisor
4,505
1,447
I think what you did is correct. If you think of them as matrices, remember they are identity matrices, so they commute with everything, so the order does not matter.
 

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