The discussion focuses on the integration of solid angles represented by ##d\Omega## in the context of vector products involving unit vectors. Participants explore the integrals ##\int d\Omega n_{i}n_{j}## and ##\int d\Omega n_{i}n_{j}n_{k}n_{l}##, questioning the validity of the expressions and suggesting that the results may relate to symmetrized products of Kronecker deltas. The consensus is that a deeper understanding of the solid angle element ##d\Omega## is essential for proper evaluation of these integrals.
PREREQUISITESMathematicians, physicists, and students studying vector calculus or tensor analysis, particularly those interested in solid angle integration and its applications in theoretical physics.
Actually, I think it should be proportional to some symmetrized product of kronecker deltas. But how can one show that?BvU said:Not if you don't provide some more context. The way it looks now (to me) it's nonsense (##n_in_j = \delta_{ij}## ? )
First you have to show what you mean. Isn't a unit vector a constant of the integration ?PreposterousUniverse said:But how can one show that?