- 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
The quantum field theoretic path integral of interacting quantum fields is analytically ill-defined and yet it is a very successful tool for predicting experimental data. What gives?
Much of the perturbative structure of QFT may ultimately be combinatorial in nature and for that reason insensitive to analytic issues. Indeed, with my collaborators D.M. Jackson and A. Morales, I showed that for example a key property of the QFT path integral, whose conventional derivation involves an analytically ill-defined Legendre transform, can be combinatorially proven (namely the fact that the Legendre transform of the effective action yields the sum of connected graphs and vice versa).
- D. M. Jackson, A. Kempf, A. Morales, On the Structure of QFT in the Particle Picture of the Path Integral Formulation, arxiv/0810.4293