## Geometry Seminar - Abstracts

### Talk

Tuesday 25 June 2019, 16:00-17:00 in HG00.308

**Matthias Lienert** (Tübingen)

*Multi-time wave equations*

### Abstract

The basic object in quantum physics is a wave function which
usually depends on one time variable and \(N\) space variables for \(N\)
particles. However, such an object is not covariant under the
Poincare group, the basic symmetry group of (special)
relativity. A straightforward generalization which fixes this
problem is to let the wave function \(\psi = \psi(x_1,...,x_N)\) depend
on one spacetime variable \(x_i\) per particle. Because of the
presence of \(N\) time variables \(t_i = x_i^0, i = 1,2,...,N\) \(\psi\) is
called a "multi-time wave function". As natural as this concept
may sound, one is led to a range of challenging physical and
mathematical problems, such as: How can one define a consistent
and interacting time evolution in the multiple time \((x_i^0)\)
variables? Which types of PDEs work for that? What is the physical
meaning of \(|\psi|^2\) at unequal times?, and: Are there new
possibilities for evolution equations which are specific to the
multi-time formalism? This talk will provide a non-technical
overview of recent progress concerning these questions.

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