I was studying how to define, formally, an energy-momentum tensor for a point particle.

I was reading this two references:http://academic.reed.edu/physics/courses/Physics411/html/page2/files/Lecture.19.pdf , page 1; and http://th-www.if.uj.edu.pl/acta/vol29/pdf/v29p1033.pdf page 1038.

They both start from an action that I understand, it's just the action for a particle moving in space time. They, then, differentiate the action with respect to the metric to get the energy-momentum tensor, but then, somehow, they arrive at an expression that has the dirac delta in it...

Can anyone help me out?

Thank you