1.8 Tensors again

Question 1

What is the rank of a tensor?

Answer 1

The number of space time indices

Question 2

What is a rank 0 tensor?

Answer 2

No index so it is a scalar

- Can also get them if all indices are summed over

Question 3

What is a rank 1 tensor?

Answer 3

A 4 vector

Question 4

What are two examples of a rank 2 tensor?

Answer 4

Metric tensor, g^(mu nu)

Faraday tensor F^(mu nu)

Question 5

What is a rank 3 tensor example?

Answer 5

Acting with a derivative on a rank 2 tensor e.g

𝛿_lambda F^(mu nu)

Question 6

Give two examples of a rank 4 tensor

Answer 6

Riemann Tensor R^(alpha, beta, gamma, delta)

Antisymmetric tensor epsilon(alpha, beta, gamma, delta)

Question 7

What is the metric tensor, g_(mu nu) useful for?

Answer 7

Converting between the covariant x_mu to the contravariant x^mu
x_nu = g_(mu nu) x^mu

Question 8

Which metric tensor do we restrict ourselves to in SR?

Answer 8

A 4x4 matrix with 1, -1, -1, -1 on the diagonal and zeroes everywhere else