Geometry Seminar - Abstracts


Tuesday 25 June 2019, 16:00-17:00 in HG00.308
Matthias Lienert (Tübingen)
Multi-time wave equations


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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