# Why using time-ordering causality? and what is Difference between Locality and Causality?

In QFT, the time-ordering causality is generally used.

There are 4 ways to bypassing the pole called time-ordering, anti-time-ordering, retarded and advanced.

But in many case only time-ordered causality is used.

Could I ask the reason why? (Source in the future couldn't affect something in the past? or just convention?)

In Srednicki QFT book, and also in Bjorken RQM book, deriving the Relativistic version of the Schrödinger equation, from the Einstein energy momentum reaction, one could get $$H \psi = \sqrt{ p^{2} +m^{2}} \psi$$. By Taylor expanding the sqrt part, there is infinite-order of Laplacian, so the theory is non-local. why is the theory non-local with the infinite-order of laplacian?

What is the local theory? and Why should the locality be kept? (is it related the Dirac light cone?)

Does one can tell that one theory is local or non-local in classical theories?

• Locality is manifested in the action itself. When we write action in terms of fields, fields are at the same position. Examples are like scalar fields. But if we require our theory should respect relativity, then we need causality. It means signal can't go past outside the lightcone. So that is the reason we use Feynman propgator in which particles and anti particles move forward in time. – Hare Jun 27 at 23:58
• We use time-ordered propagators for some calculations and retarded/advanced for others. The question you should be asking is what these different propagators compute. The reason time-ordered propagator is commonly used is that the perturbation theory is most conveniently formulated using it. – Peter Kravchuk Jun 28 at 4:06
• Thank you for your coments! – Summal Jun 28 at 5:25