Global analysis and geometry of Lorentzian manifolds

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In the attempts of unifying quantum theory and general relativity theory one was able to quantize certain types of fields on curved spacetimes (i.e. Lorentzian manifolds) which were most relevant from the physical point of view. The aim of the proposed project is to develop a unified and systematic approach to this kind of quantization. This would in particular avoid having to repeat similar work in the quantization procedure for every new physically relevant field.