- #1
Cosmology2015
- 31
- 1
Hello,
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 .
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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