- #1

- 117

- 17

- Homework Statement
- Expressing the field tensor in terms of the four dimensional Levi-Civita symbol and covariant dual field tensor.

- Relevant Equations
- See solution.

Exercise:

Solution:

The result is correct, but I'm unsure about equation from 29 to 30 where right-hand side became just the covariant dual field tensor. I assumed that I could interchange the covariant dual- and normal covariant field tensor, but don't think it's possible since matrices aren't commutative.

I think I bruteforced to get the correct result.

P.S: definition (20) is just the definition of the four-dimensional Levi-Civita symbol.

Solution:

The result is correct, but I'm unsure about equation from 29 to 30 where right-hand side became just the covariant dual field tensor. I assumed that I could interchange the covariant dual- and normal covariant field tensor, but don't think it's possible since matrices aren't commutative.

I think I bruteforced to get the correct result.

P.S: definition (20) is just the definition of the four-dimensional Levi-Civita symbol.