epsilon delta?

**revolution2000** · May 2nd 2009, 04:18 AM

The epsilon delta rule states

EijkEpqk=(delta(ip)delta(jq)-delta(iq)delta(jp))

I am constantly using this but get stuck when it is applied.

For example

EijkEpqkA(j)B(l)C(m)=(delta(ip)delta(jq)-delta(iq)delta(jp))A(j)B(l)C(m)

This then becomes

A(j)B(i)C(j)-A(j)B(j)C(i)

Can anybody please explain this result????

**VonNemo19** · May 2nd 2009, 08:26 AM

I think you may have had some trouble when you did your latex, because I can't understand a word of what you wrote. My specialty is epsilon-delta proofs so I would love to help. Let me know when you fix the glitch.

**revolution2000** · May 2nd 2009, 10:00 AM

do you mean writing it in math type. I don't know how to do that.
Is there an option on the posting screen?

**revolution2000** · May 2nd 2009, 10:09 AM

The epsilon delta rule states

$\epsilon_{ijk}\epsilon_{pqk}=\delta_{ip}\delta_{jq }-\delta_{iq}\delta_{jp}$

I am constantly using this but get stuck when it is applied.

For example

$\epsilon_{ijk}\epsilon_{pqk}A_{j}B_{l}C_{m}=(\delt a_{ip}\delta_{jq}-\delta_{iq}\delta_{jp})A_{j}B_{l}C_{m}$

This then becomes

$A_{j}B_{i}C_{j}-A_{j}B_{j}C_{i}$

Can anybody please explain this result????

Is it true that

$\delta_{ij}a_{i}=a_{j}$

If so does this not apply to the above

Thank you for your reply

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