Speaker
Description
In this talk, we present recent progress on applying efficient, deep-learning-inspired numerical techniques to solving quantum constraints in canonical loop quantum gravity (LQG) models. Focusing on the 4-dimensional weak coupling model of LQG, we approximate and analyse physical solutions of the Thiemann regularised quantum Hamilton constraint and characterise their structure and physical properties. To name a few, we show that such solutions exhibit long-range correlation, we investigate their normalisability and the geometries which they represent. We also demonstrate how different constraint orderings can be systematically compared.
We illustrate the broader applicability of this approach to a range of LQG settings, including quantum reduced loop gravity and selected spherically symmetric models. Finally, we show that in principle, the developed methods enable large-scale simulations of graph-non-enlarging LQG models with arbitrarily large cutoffs on the degrees of freedom and arbitrarily complex underlying graphs, all at tractable computational cost. We conclude with an outlook and roadmap for extending this programme to full SU(2) models and potentially to genuinely graph-changing dynamics.
