Math

Introduction Lie groups and Lie algebras form the backbone of modern physics and mathematics, particularly in areas such as quantum mechanics, particle physics, and differential geometry. A Lie group is a continuous group with a smooth structure, where elements can be parameterized by continuous variables. These groups encapsulate symmetries of physical systems and are often … Read more

The group discussed here, also known as the Lorentz group in one dimension, describes the symmetries of special relativity with one spatial and one temporal dimension. The metric is defined as: \[\eta = \begin{pmatrix}1 & 0 \\0 & -1\end{pmatrix}\] The position vector is given by: \[x = \begin{pmatrix}ct \\x\end{pmatrix}\] If \(x\) transforms as \(x’ = … Read more