Editing Propagator (section)

====Positive and negative frequency parts (cut propagators)====
We can define the positive and negative frequency parts of <math>\Delta(x-y)</math>, sometimes called cut propagators,  in a relativistically invariant way.

This allows us to define the positive frequency part:
:<math>\Delta_+(x-y) = \langle 0 | \Phi(x) \Phi(y) |0 \rangle, </math>

and the negative frequency part:
:<math>\Delta_-(x-y) = \langle 0 | \Phi(y) \Phi(x) |0 \rangle. </math>

These satisfy<ref name="BD"/> 
:<math>\,i \Delta = \Delta_+ - \Delta_-</math>

and
:<math>(\Box_x + m^2) \Delta_{\pm}(x-y) = 0.</math>