Free wave equation: Difference between revisions

Revision as of 14:38, 20 June 2009

The free wave equation on ${\mathbb {R} }^{1+d}$ is given by

\Box f=0

where f is a scalar or vector field on Minkowski space ${\mathbb {R} }^{1+d}$ . In coordinates, this becomes

-\partial _{tt}f+\Delta f=0.

It is the prototype for many nonlinear wave equations.

One can add a mass term to create the Klein-Gordon equation.

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-The '''free wave equation''' on <math>R^{1+d}</math> is given by
+The '''free wave equation''' on <math>{\mathbb R}^{1+d}</math> is given by
 <center><math>\Box f = 0</math></center>
-where ''f'' is a scalar or vector field on [[Minkowski space]] <math>R^{1+d}</math>.
+where ''f'' is a scalar or vector field on [[Minkowski space]] <math>{\mathbb R}^{1+d}</math>.
 In coordinates, this becomes
 <center><math>- \partial_{tt} f + \Delta f = 0.</math></center>