Idea of the Spring School
The Spring School is particularly suitable for Master and PhD students in mathematical and theoretical physics.
It provides the opportunity to learn more about a new and interesting topic at the intersection of quantum theory and relativity.
Multi-time wave functions
were first suggested by Dirac in 1932 but investigated in detail only in recent years. The key idea is to study, for N quantum particles, a wave function psi(x_1,...,x_N) where each x_i is a spacetime point. One arrives at a new and manifestly covariant picture of quantum theory. Contrary to the usual wave function of Schrödinger's equation, psi then depends on many times which opens up several interesting mathematical and physical questions, such as:
- Which evolution equations for psi are appropriate?
- In which cases are these equations consistent?
- How can one implement interaction?
- Can one re-formulate quantum field theory using multi-time wave functions?
- What is the relation of psi with physical experiments? Does |psi|^2 represent a probability density?
In the Spring School, we will develop the topic of multi-time wave functions from scratch, answering the above-mentioned questions. Exercise sessions will complement the lectures. Prerequisites are: background knowledge of calculus, quantum mechanics, and relativity.
The topics of the lectures
- consistency conditions
- inconsistency of potentials
- examples of consistent multi-time evolution with interaction
- connection with quantum field theory and the Tomonaga-Schwinger equation
- multi-time integral equations
- |psi|^2 and detection probability for detectors placed along a spacelike hypersurface
April 10, 13:30 - April 12, 16:00, 2019
University of Tübingen
Campus Auf der Morgenstelle, C-building (Fachbereich Mathematik), room N14 (ground floor). How to get there
please send an email
February 28, 2019
Organizers: Matthias Lienert
and Roderich Tumulka
Funding: External participants
can apply for a contribution towards their traveling and accommodation expenses. Please indicate if you wish to apply in your registration email.
Accommodation for external participants
Participants are expected to make their own arrangements for accommodation. In the city center of Tübingen, there are many hotels which are well-connected to public transport. The DJH Youth Hostel
is a particularly affordable option.
This project has received funding from the European Union's Framework for Research and Innovation "Horizon 2020" (2014-2020) under the Marie Sklodowska-Curie Grant Agreement No. 705295.