Editing Propagator (section)

====Pauli&ndash;Jordan function====
The commutator of two scalar field operators defines the [[Wolfgang Pauli|Pauli]]&ndash;[[Pascual Jordan|Jordan]] function <math>\Delta(x-y)</math> by<ref>{{Cite journal |last1=Pauli |first1=Wolfgang |last2=Jordan |first2=Pascual |year=1928 |title=Zur Quantenelektrodynamik ladungsfreier Felder |journal=Zeitschrift für Physik |volume=47 |issue=3–4 |pages=151–173|doi=10.1007/BF02055793 |bibcode=1928ZPhy...47..151J |s2cid=120536476 }}</ref><ref name="BD">{{Cite book |last1=Bjorken |first1=James D. |title=Relativistic Quantum Fields |last2=Drell |first2=Sidney David |publisher=[[McGraw-Hill]] |year=1964 |isbn=978-0070054943 |series=International series in pure and applied physics |location=New York, NY |chapter=Appendix C}}</ref>

:<math>\langle 0 | \left[ \Phi(x),\Phi(y) \right] | 0 \rangle = i \, \Delta(x-y)</math>
with
:<math>\,\Delta(x-y) = G_\text{ret} (x-y) - G_\text{adv}(x-y)</math>

This satisfies 
:<math>\Delta(x-y) = -\Delta(y-x)</math> 
and is zero if <math>(x-y)^2 < 0</math>.