In a similar way one can describe the 10-momentum introduced in Section 1.9 by means of a symmetric covariant spinor that transforms according to a different inequivalent representation of \begin{equation}
._1x9diBHPBP-hL1JiwUwJ5J{font-size:14px;font-weight:500;line-height:18px;color:#ff585b;padding-left:3px;padding-right:24px}._2B0OHMLKb9TXNdd9g5Ere-,._1xKxnscCn2PjBiXhorZef4{height:16px;padding-right:4px;vertical-align:top}._1LLqoNXrOsaIkMtOuTBmO5{height:20px;padding-right:8px;vertical-align:bottom}.QB2Yrr8uihZVRhvwrKuMS{height:18px;padding-right:8px;vertical-align:top}._3w_KK8BUvCMkCPWZVsZQn0{font-size:14px;font-weight:500;line-height:18px;color:var(--newCommunityTheme-actionIcon)}._3w_KK8BUvCMkCPWZVsZQn0 ._1LLqoNXrOsaIkMtOuTBmO5,._3w_KK8BUvCMkCPWZVsZQn0 ._2B0OHMLKb9TXNdd9g5Ere-,._3w_KK8BUvCMkCPWZVsZQn0 ._1xKxnscCn2PjBiXhorZef4,._3w_KK8BUvCMkCPWZVsZQn0 .QB2Yrr8uihZVRhvwrKuMS{fill:var(--newCommunityTheme-actionIcon)} We will call the multiplication in this algebra the geometric product. \nabla \psi' R I_3 \tilde{R}+ m \psi' = 0. Next, if V*1,...,Vn* are n vector spaces over R or C, then I can create multivariable functions that take in a vector from each of them and output a real (or complex) number. Tensor is the generalized form of vectors and scalars. \end{equation} Do you happen to know if there is a good mathematical._3U-J6NPoBHbyibarrb7T3F{font-size:14px;font-weight:700;letter-spacing:.5px;line-height:32px;text-transform:uppercase;display:block;padding:0 16px;width:100%;margin-top:10px}.FIYolDqalszTnjjNfThfT{max-width:256px;white-space:normal;text-align:center} You're just writing it different, but nothing has actually changed. Now, it turns out that a rotation of the vector $v$ in the plane defined by a simple bivector $\omega$ by $|\omega|$ radians (where the absolute value is $\sqrt{-\omega^2}$, since the square of $\omega$ is negative) can be expressed in geometric algebra (GA) as. The Dirac field $\psi$ takes values in the even subalgebra of the geometric algebra. 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