- #1
center o bass
- 545
- 2
Hello! I'm reading up on Hamiltonian mechanics and i stumbled on the fact that the curl of the vector potential can be expressed as
B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j}
Now the text that I'm reading says that this formula can be inverted as
\sum_k \epsilon_{kij} B_k = \frac{\partial A_j}{\partial x_i} - \frac{\partial A_i}{\partial x_j}
But I then wondered how this inversion would be accomplished?
I suspect the formula \sum_k \epsilon_{kij} \epsilon_{klm}= \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl} to be involved.
B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j}
Now the text that I'm reading says that this formula can be inverted as
\sum_k \epsilon_{kij} B_k = \frac{\partial A_j}{\partial x_i} - \frac{\partial A_i}{\partial x_j}
But I then wondered how this inversion would be accomplished?
I suspect the formula \sum_k \epsilon_{kij} \epsilon_{klm}= \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl} to be involved.
