The d'Alembertian is a linear second order differential operator, typically in four independant variables. The time-independant version (in three...
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The d'Alembertian is a linear second order differential operator, typically in four independant variables. The time-independant version (in three independent (space) variables is called the Laplacian operator. When it's action on a function or vector vanishes, the resulting equation is called the wave equation (or Laplace's equation). When it's action is identified with a non-zero function (or vector function) the resulting equation is called Poisson's equation. This equation is fundamental to and of great importance in field theory. The focus of this tutorial is to demonstrate that when acting on a four-vector, the d'alembertian may be factored into two 4x4 differential matrices.