NWO M-1 grant for Oliver Fabert

The Dutch Research Council (NWO) has awarded Oliver Fabert an Open Competition Domain Science M-1 grant for his research project “Floer theory for stochastic Hamiltonian systems, quantum theory, and imaginary time”, worth 350,000 Euros for 4 years to fund one PhD position. Hamiltonian Floer theory and pseudoholomorphic curves are well-established elliptic methods in symplectic geometry. Traditionally applied to problems from classical physics, this proposal seeks to extend their utility to quantum physics through stochastic Hamiltonian systems. The committee awarded the scientific quality of his proposal the highest grade (“excellent”), and his research proposal even ranked first among the 30 research proposals processed together with his proposal.

The core theoretical concept introduced in Stephen Hawking’s world-bestseller “A Brief History of Time” is the idea of imaginary time. Although he admits that it very likely has no reality, he praises this concept as it allows to circumvent severe mathematical problems that appear in physical models such as the quantum mechanical description of black holes. In more scientific terms, it describes a surprising link, called Wick rotation, between quantum field theory and classical statistical mechanics via the method of analytical continuation from complex analysis. Apart from turning the hyperbolic wave equation into the elliptic Laplace equation, by linking the Schrödinger equation with the classical heat or diffusion equation it allows to approach problems in quantum physics using probabilistic methods. While for classical mechanics there exist so-called elliptic methods from symplectic geometry such as Hamiltonian Floer theory and pseudoholomorphic curves to find solutions with special properties, passing from mechanics to field theory or from classical to quantum these methods are not readily applicable. It is the goal of this grant to explore the concept of imaginary time and stochastic approaches for generalising elliptic methods from classical mechanics to quantum mechanics and quantum field theory.