5. Identify the free and dummy indices in the following equations and change them into equivalent expressions with different indices. How many different equations does each expression represent? (a) $A^\alpha B_\alpha$; (b) $A'^\alpha = \Lambda^\alpha \_\beta A^\beta$; (c) $T_{\alpha \mu \lambda} A^\mu C^\lambda = D^\alpha$.
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To change the dummy index, we can replace b with any other letter, for example, c. The equivalent expression is AºCa. The expression represents one equation. Show more…
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