Kronecker Delta: A Relativity and Tensor Explanation

[Terilien]

I keep seeing this come up in relativity and tensor resources but I have no idea wht the heck it means. Could someone explain it to me?

 

[whatta]

diagonal ones

 

[pmb_phy]

I keep seeing this come up in relativity and tensor resources but I have no idea wht the heck it means. Could someone explain it to me?

The Kronecker delta is a function of two integers. If the integers are the same then the value of the function is 1. Otherwise it is zero. This function can be represented as a matrix. The notation for this function is $\delta$_ij.

Pete

 

[Terilien]

The Kronecker delta is a function of two integers. If the integers are the same then the value of the function is 1. Otherwise it is zero. This function can be represented as a matrix. The notation for this function is $\delta$_ij.

Pete

Why is it important in tensor analysis?

 

[George Jones]

Example from relativity. Let the coordinates of an event be $\left\{x^0 , x^1 , x^2 , x^3 \right\}.$ Then, using the summation convention of summing over repeated indices,

$$x^\mu \delta_{\mu \nu} = x^0 \delta_{0 \nu} + x^1 \delta_{1 \nu} + x^2 \delta_{2 \nu} + x^3 \delta_{3 \nu}.$$

Since the Kronecker delta is zero unless both indices are equal, only one of the terms in the above sum survives. We don't know which one, but we know it's the one that has $\nu$ as its first index. Therefore, the sum equals $x^\nu .$

 

[whatta]

Why is it important in tensor analysis?

because it's a metric tensor of euclidean space? dunno. the "importance" asigned to things by different people is quite biased.