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When the indices are the same in both terms in a product, it means the product is summed/repeated over all the coordinates. When they are different, they are only counted once. Is that helpful?John Fennie said:
Some authors (I know Schwartz does and mentions it in the preface of his QFT book) find it so obvious that repeated indices should be contracted using the metric that they resort to writing all indices in one position.dextercioby said:
Hi yes, i understand that. But I am unable to work the math out, specifically the second +$\frac{1}{2}$John Fennie said:
The purpose of calculating indices in "Solve the Mystery" is to determine the unknown values in a given equation or problem. This helps to solve the mystery or puzzle presented in the activity.
Indices are calculated by using the laws of indices, also known as exponent rules. These rules include multiplying indices with the same base, dividing indices with the same base, and raising a power to a power. It is important to follow the correct order of operations when calculating indices.
Some common mistakes when calculating indices include forgetting to apply the rules of indices, using the wrong base or exponent, and mixing up the order of operations. It is important to double-check your work and make sure all rules are properly applied.
Calculating indices is useful in many real-life situations, such as in finance and science. In finance, indices are used to track the performance of stocks and investments. In science, indices are used to represent large or small numbers, as well as in calculating rates of change and growth.
Some tips for solving tricky index problems include simplifying the expression as much as possible, breaking down the problem into smaller steps, and checking your work by plugging in values or using a calculator. It is also helpful to practice regularly and familiarize yourself with the laws of indices.
