Problem 7 Prove the e-8 identity Eyjk Eijs = 0; Os - O; Op Hint: two of the four free indices jkrs must be equal. Show f

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Problem 7 Prove The E 8 Identity Eyjk Eijs 0 Os O Op Hint Two Of The Four Free Indices Jkrs Must Be Equal Show F 1 (43.37 KiB) Viewed 84 times

Problem 7 Prove the e-8 identity Eyjk Eijs = 0; Os - O; Op Hint: two of the four free indices jkrs must be equal. Show first that ifj=k or r=s, then both sides vanish identically (For example, Eikt = 0 and 8083708)s -03)502) = 0, where the parentheses around k are used to indicate that there is no sum on k.) Then show that even with j #k and r #s, both sides vanish when j=r unless also k=s, and then prove that E:(}(*) Ex()(x) = 0(r)()Ox)(x) - 07/(x) Oryck) for r #k. What cases remain to consider?