- #1
Jyoti6297 said:I didn't get the last part.
So the permutation symmetry of the ##()## is the same as of the Levi-Civita, so we can
##()_{\mu\sigma\eta\nu}=\epsilon_{\mu\nu\eta\sigma} ()_{1234} = \epsilon_{\mu\nu\eta\sigma} \cdot \epsilon_{\alpha\beta\gamma\kappa}A^\alpha_1 A^\beta_2 A^\gamma_3 A^\kappa_4 ##
Do you mean
##()_{\mu\nu\eta\sigma}## instead of ##()_{\mu\sigma\eta\nu}## here? Or am I interpreting something wrong?
Levi Civita is pronounced "LEH-vee chee-VEE-tah".
Levi Civita (1873-1941) was an Italian mathematician known for his contributions to tensor calculus and differential geometry.
The Levi-Civita symbol, also known as the permutation symbol, is a mathematical symbol used to represent the sign of a permutation of a set of numbers. It is commonly denoted by the Greek letter epsilon (ε).
Levi Civita's work on tensor calculus and differential geometry was essential to the development of Einstein's theory of general relativity. He helped Einstein formulate the mathematical equations that describe the curvature of spacetime.
Levi Civita's work has applications in various fields such as physics, engineering, and computer science. You can use his theories and equations to solve problems related to differential geometry, tensor calculus, and general relativity.