Visualizing Imaginary Rotations and Applications in Physics

Abstract

I discuss the notions of traditional vector length, and suggest defining a complex vector length for complex vectors, as opposed to the traditional Hermitian real length. The advantages of this are shown in the development of rotations through imaginary angles. Emphasis is placed on visualizing these quantities and rotations graphically, and I show some applications in physics: Lorentz transformations, Grassmann variables, and Pauli spin matrices.