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

PDF
Lienert_Matthias.pdf 1MB 
Abstract
The present work deals with the idea of a multitime wave function, i.e. a wave function with N spacetime arguments for N particles. Firstly, a careful derivation of the necessity of multitime wave functions in relativistic quantum mechanics is given and a general formalism is developed. Secondly, the physical meaning of multitime wave functions is discussed in connection with realistic relativistic quantum theories, in particular the "Hypersurface BohmDirac" model. Thirdly, a first interacting model for multitime wave functions of two Dirac particles in 1+1 spacetime dimensions is constructed. Interaction is achieved by means of boundary conditions on configuration spacetime, a mechanism closely related to zerorange 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 Nparticle case. Higher dimensions are also discussed. Finally, the "TwoBody Dirac equations" of constraint theory are placed within the context of the multitime formalism. In particular, the question of probability conservation is critically discussed, leading to further implications both for fundamental and applied questions.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  multitime wave functions, relativity theory, relativistic wave equations, construction of rigorous interacting relativistic models, realistic relativistic quantum theories 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  16. September 2015 
1. Referee:  Dürr, Detlef 
Persistent Identifier (URN):  urn:nbn:de:bvb:19187057 
MD5 Checksum of the PDFfile:  96231003ee665e26d3d32b7f796eda5e 
Signature of the printed copy:  0001/UMC 23292 
ID Code:  18705 
Deposited On:  21. Oct 2015 13:54 
Last Modified:  21. Oct 2015 13:54 