Might there be a similarity between Dyson's equation and Heisenberg equation? (It's just a feeling, nothing based on arguments.) Both describe how a system (density matrix or Green's function) behaves in time. Both require knowledge of the intial system at time t=0 and the potential acting on the system.(adsbygoogle = window.adsbygoogle || []).push({});

The Dyson equation:

[tex] G = G_0 + G_0 V G[/tex] usually solved with the iteration steps [tex] G_{j+1} = G_0 + G_0 V G{j}[/tex]

The Heisenberg equation of motion (with the density as the operator):

[tex] \rho = U^{\dag} \rho_0 U{ [\tex] with [tex] U = e^{\frac{-i}{\hbar} H t[\tex] (in the case of a time independent Hamiltonian).

There must be bridge, but I can't find a mathematical transition or a common ground. My knowledge on Green's function is just too limited.

Does anybody has an idea what could lead in the right direction?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Connection between Dyson's equation and Heisenberg equation of motion

Loading...

Similar Threads for Connection between Dyson's |
---|

B The setup of "2012 entanglement between photons that (...)" |

I Correlation setup between past and present |

B Does this connect Quantum Theory and Special Relativity? |

A Berry phase and parallel transport |

A Is the Berry connection compatible with the metric? |

**Physics Forums | Science Articles, Homework Help, Discussion**