Hamburg 2016 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Von der Gravitation zur Quantengravitation

MP 8.3: Talk

Thursday, March 3, 2016, 11:20–11:40, VMP6 HS B

The Poincaré Symmetric String — Norbert Dragon and •Florian Oppermann — Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover

Using the toy model of the free bosonic string we discuss Poincaré symmetric quantum theories with maps between massless and massive states.

In String Theory these maps are given by creation and annihilation operators α_n^µ which generate the Fock space and therefore connect states on different mass shells. When examined carefully the commutator relations lead to contradictions in most quantization schemes, namely empty physical Hilbert spaces, negative mass shells and problems with Lorentz generators.

It can be seen that these problems don’t occur due to the method of quantization but because of a fundamental difference between massive and massless states. The Mackey theory of unitary representations of the Poincaré group shows that the latter cannot be described by global momentum wave functions (except in D=3, 5, 9) but need local sections in a bundle.