causal propagator | | ![](https://ncatlab.org/nlab/files/AdvancedGreenFunction.png) | | Peierls-Poisson bracket |
advanced propagator | | ![](https://ncatlab.org/nlab/files/RetGreenFunction.png) | | future part of Peierls-Poisson bracket |
retarded propagator | | ![](https://ncatlab.org/nlab/files/AdvancedGreenFunction.png) | | past part of Peierls-Poisson bracket |
Wightman propagator | | ![](https://ncatlab.org/nlab/files/HadamardPropagator.png) | | positive frequency of Peierls-Poisson bracket, Wick algebra-product, 2-point function of vacuum state or generally of Hadamard state |
Feynman propagator | | ![](https://ncatlab.org/nlab/files/FeynmanPropagator.png) | | time-ordered product |