Study of randomness of geometry resulting from quantum fluctuations

We are pleased to announce that another work The impact of a random metric upon a diffusing particle in the field of quantum gravity was published by prof. dr hab. Zbigniew Haba in the prestigious journal Scientific Reports.

‘The motivation for this work was quantum gravity,’ prof. Haba explains. ‘While a satisfactory quantum gravity theory does not exist, it can probably be understood as the randomness of geometry resulting from quantum fluctuations. We imagine that fluctuations will increase on small distances. With these assumptions, it is possible to study what the effect of those fluctuations in geometry will be on the matter fields.’

The animation shows a visualization of quantum fluctuations. Source: Wikipedia

‘Quantum fields are described by correlation functions that depend on the metric on Riemannian space-time,’ says prof. Haba. ‘By standard mathematical methods, these correlation functions can be represented by a diffusion process on Riemannian spacetime. Averaging over the metric fluctuations, we obtain the observable matter field correlations.’

‘In my work I showed that singular over small distances correlations of metrics lead to faster diffusion growth for small times,’ prof. Haba continues. ‘In consequence, correlations of fields on small distances are more regular. My goal was to realize the suggestion by Pauli and Landau (from the beginnings of quantum field theory) that once gravity is quantized, quantum field theory will not have difficulties related to discrepancies at small distances, requiring a dubious renormalization method.