The mosaic tiles of quantum gravity


Understanding the quantum structure of spacetime is one of the most challenging open problems in physics. It requires the combination of the two central paradigms of modern physics: general relativity and quantum theory, giving rise to a theory of quantum gravity answering age-old questions about the origin of the universe and the nature of black holes singularities. So far, the construction of such a theory using the successful techniques applied to the other fundamental interactions led to inconsistencies and new perspectives are required. A peculiar aspect is that the entity to be quantized is the geometry of spacetime. Following Feynman’s quantization prescription, one has to “sum over geometries”. The route I take in this project is to discretize geometry and sum over all possible discrete “surfaces”. The resulting physical theory is obtained by taking the continuum limit, i.e., by taking the discretization scale to zero while increasing the number of building blocks. One searches for a suitable dynamics which drives these “spacetime tiles” to form a large-structure which resembles our universe. I will investigate if and how a well defined continuum limit can be taken in different approaches to quantum gravity. The main tool I will employ is the renormalization group which allows one to probe physics at different length scales, very much like a “microscope”. Recently, I developed renormalization group techniques suitable for coarse-graining theories of quantum geometry. This constitutes an extremely versatile toolbox which will allow me to explore synergies between different discrete approaches to quantum gravity and extract universal properties a consistent theory of quantum gravity should feature. This paves the way for my quest of finding suitable continuum limits for quantum gravity and establish qualitative as well as quantitative comparison between physical quantities computed within diverse approaches heading towards a complete picture of quantum spacetime.





Dr. A. Duarte Pereira Jr

Verbonden aan

Universität Heidelberg


01/09/2019 tot 31/08/2022