Lienert, Matthias (2015): Lorentz invariant quantum dynamics in the multi-time formalism. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics |

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**DOI**: 10.5282/edoc.18705

### Abstract

The present work deals with the idea of a multi-time wave function, i.e. a wave function with N space-time arguments for N particles. Firstly, a careful derivation of the necessity of multi-time wave functions in relativistic quantum mechanics is given and a general formalism is developed. Secondly, the physical meaning of multi-time wave functions is discussed in connection with realistic relativistic quantum theories, in particular the "Hypersurface Bohm-Dirac" model. Thirdly, a first interacting model for multi-time wave functions of two Dirac particles in 1+1 space-time dimensions is constructed. Interaction is achieved by means of boundary conditions on configuration space-time, a mechanism closely related to zero-range physics. This is remarkable, as a restrictive consistency condition rules out various types of interaction and consequently no rigorous interacting model was known before. Fourthly, the model is extended to more general types of interaction and to the N-particle case. Higher dimensions are also discussed. Finally, the "Two-Body Dirac equations" of constraint theory are placed within the context of the multi-time formalism. In particular, the question of probability conservation is critically discussed, leading to further implications both for fundamental and applied questions.

Item Type: | Theses (Dissertation, LMU Munich) |
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Keywords: | multi-time wave functions, relativity theory, relativistic wave equations, construction of rigorous interacting relativistic models, realistic relativistic quantum theories |

Subjects: | 500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 16. September 2015 |

1. Referee: | Dürr, Detlef |

MD5 Checksum of the PDF-file: | 96231003ee665e26d3d32b7f796eda5e |

Signature of the printed copy: | 0001/UMC 23292 |

ID Code: | 18705 |

Deposited On: | 21. Oct 2015 13:54 |

Last Modified: | 23. Oct 2020 21:35 |