Professor Andreas Fring
School of Engineering and Mathematical Sciences
Though mathematical physics is most commonly understood as the application of mathematics and mathematical methods to problems in physics, Professor Fring points out that in this area of research, the theories and applications of physics can equally inform and inspire mathematics. Since the time of Isaac Newton, mathematical physicists have made significant contributions to the two disciplines that give the field its name. The mathematical physics group at City, headed by Professor Fring and located within the School of Engineering and Mathematical Sciences, is renowned for its work on quantum mechanics, quantum field theory and string theory.
Professor Fring has particular expertise in quantum field theory, an area of mathematical physics that was the focus of his doctoral thesis and much of his early post-doctoral research. Quantum field theory, one of the cornerstones of modern theoretical physics, explores how the laws of quantum mechanics, which govern the world of atoms and elementary particles, can be combined with relativity, the other pillar of twenty-first century theoretical physics, which governs the behaviour of the large structures of the universe. Within this broad subject area, Professor Fring focuses on models that are integrable (models that can be solved exactly) in one time and one space dimension. Such models are very special, as most models in higher dimensions can be solved only approximately. Working with such explicitly 'knowable' models in one time and one space dimension provides deep insights into the fundamental principles of physics. Professor Fring is an active participant in the global network of mathematical physicists working on quantum field theory and City University London has hosted several conferences focused on this area of research.
One difficulty of quantum field theory that challenged physicists for much of the early twentieth century was the occurrence of infinitely large physical quantities. In seeking to resolve this issue, physicists developed the idea of non-commutative spacetime, which offered a means of removing the infinite quantities, but in so doing presented a new challenge: in many cases the theories violated the mathematical concept of Hermiticity which was thought to be essential for a theory to describe the real physical world adequately. Only recently it has been discovered that Hermiticity is not always a necessary requirement for a physical theory. This discovery has led to a new area of research in which Professor Fring is very active. Most recently, he co-ordinated an international workshop on quantum physics and non-Hermitian operators at the Max Planck Institute in Dresden.
If much of Professor Fring's work on quantum field theory, non-commutative spacetime and non-Hermitian models is concerned with the theoretical fundamentals of physics, his work on high-intensity laser physics is more applied, with implications for scientists from other fields of research. The team of mathematical physicists at City focuses on several phenomena occurring in the context of high-intensity laser physics, including high-order harmonic generation and atomic stabilization, both of which provide valuable opportunities for physicists, chemists and biologists to test their methods.