Workshop

The classical Feynman integral gives the transition amplitude for a quantum particle to move from one space-time point to another. The integral extends over the space of continuous paths joining these two points. Feynman's approach to quantum evolution put paths into mechanics on the quantum level and so represented a viewpoint that was distinctly different from the traditional one. This highly oscillatory infinite dimensional integral is far from being a part of the absolutely convergent Lebesgue theory; in fact, interference effects are the key. Substantial progress, some of it recent, has been made in the mathematically rigorous theory of the Feynman integral. Heuristic Feynman integrals have led or contributed to exciting advances in recent years in a variety of topics in quantum theory as well as in the mathematically rigorous theories of knots and low-dimensional topology. On the physical side, heuristic Feynman-type integrals and associated perturbation expansions have become an essential tool both in theoretical and applied areas, including quantum mechanics, quantum field theory, gauge theory, quantum gravity and string theory, as well as optics and the study of macromolecules. Influence in other areas like biology and financial or electrical engineering has also increased recently. The goal of this workshop is to encourage interactions between researchers (mathematicians, physicists and other scientists) who have worked on different approaches to the Feynman integral and its related topics and applications. It is also to help graduate students, young researchers and non-experts to enter this increasingly important and cross-disciplinary subject; several introductory or bridge talks will be provided to that effect. Topics to be focused on during the workshop: -- Mathematically rigorous theories of the Feynman integral. -- Relationship between the heuristic Feynman integral and knot theory. -- Applications of heuristic Feynman integral to physics (and other areas of science). -- Relationship between the Feynman integral and quantum computing. Note: The workshop has been scheduled to end the day before the beginning of the final workshop of the MSRI Program on Quantum Computing in order to encourage interested participants from either group to explore possible connections between the two subjects.