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Before starting, I would like to apologize for any errors in the use of symbols. This is my first time .

I am studying the wonderful book of Barton Zwiebach, "A First Course in StringTheory".

In chapter 02, I am experiencing for the first time with the mathematics of special relativity (Minkowski Spacetime).

My question is on the definition of invariant interval ds[2]. By definition, the invariant interval is given by -ds[2]=η[μν]dx[μ]dx[ν]

I am not able to understand the minus sign on ds[2]. Is there any relationship with the idea of positive-definite condition? Others books use only ds[2] for the invariant interval. Is there any advantage in using this convention?

Another question would be about the invariant interval -ds[2.]. The definition of the invariant interval is very similar to the definition of Riemannian metric (metric tensor) g[ij].

(a) invariant interval → -ds[2]=η[μν]dx[μ]dx[ν]

(b) Riemannian metric → g=∑g[ij]dx⊗dx[j]

Is there any direct relationship? What is the difference between them?

I sincerely thank any reply.

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# A First Course in String Theory/Invariant Interval/Metric

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