While we all know and love momentum-space Feynman rules, sometimes we have cause to work in position space. As Lenny Susskind says, "only perverts think in momentum space." Some reasons to use position involve CFTs, curved spacetime, and possibly flat spacetime dimensions other than four.(adsbygoogle = window.adsbygoogle || []).push({});

Can anyone recommend a good reference for doing QFT calculations in position space, possibly involving a familiar theory like phi^4, QED, etc.

I tried phi^4 and ran into a problem off the bat. The generic position-space propagators are horrible, but they aren't so bad in the massless case. In fact, the position space Feynman propagator in 4d, up to a factor of +-i is:

Df(x,y) = 1/4pi delta((x-y)^2) - i/(4pi^2) sgn((x-y)^2)/(x-y)^2

and this is for lorentzian signature. Unfortunately, this has a null divergence.

I'm used to hell breaking loose at short distances, but here it happens if x and y are

simply light-like separated. The above expression already takes the i epsilon prescription into account, so I don't think it's an issue there.

In any case, any help/reference would be greatly appreciated.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Position-Space Correlators

Loading...

Similar Threads - Position Space Correlators | Date |
---|---|

I Why is position-space favored in QM? | Jan 19, 2018 |

A Transformation of position operator under rotations | Nov 27, 2017 |

A Correlation functions in position and momentum space | Oct 5, 2016 |

How to get position operator in momentum space? | Sep 27, 2015 |

Gaussian wave packet in position space | Aug 29, 2015 |

**Physics Forums - The Fusion of Science and Community**