- Quantum gravity I
- Quantum gravity II
- Relativistic quantum information
- Quantum computing
- Communication engineering
- Shannon sampling theory/data compression
- Mathematical biology
- Radar signal design for maximum information return
- The Casimir effect in layered superconductors
- Combinatorics in quantum field theory
- Further interests: Consciousness
What kind of mathematics will the unified theory of quantum gravity require?
This math will need to naturally combine the mathematical frameworks of quantum theory and general relativity, i.e., it will have to naturally combine functional analysis and differential geometry. There is a mathematical discipline that combines functional analysis and differential geometry, namely the discipline of spectral geometry. This discipline asks for example if one can hear the shape of things (curvature information) from their sound (spectral information). I have proposed that if so, one should be able to express the curvature of spacetime in terms of its quantum noise spectrum. To be able to express curvature in this way in quantum terms should be useful for quantizing curvature.
- D. Aasen, T. Bhamre, A. Kempf, Shape from sound: New tools for quantum gravity, Phys. Rev. Lett. 110, 121301 (2013)
- A. Kempf, Quantum Gravity on a Quantum Computer, arXiv:1302.3680, in print in Foundations of Physics (2013)