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The Feynman Integral Along with Related Topics and Applications December 09, 2002 - December 12, 2002
Registration Deadline: December 12, 2002 over 16 years ago
To apply for Funding you must register by: September 09, 2002 over 16 years ago
Parent Program: --
Organizers Sergio Albeverio, Cecile DeWitt-Morette, Gerald W. Johnson, Louis H. Kauffman, and Michel L. Lapidus (chair)

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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.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

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Schedule, Notes/Handouts & Videos
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Dec 09, 2002
09:15 AM - 09:45 AM
  Morning Tea
09:45 AM - 10:00 AM
  Welcome & Introduction
Loa Nowina-Sapinski
10:00 AM - 11:00 AM
  Action and symmetries
Cecile DeWitt-Morette (University of Texas, Austin)
11:00 AM - 12:00 PM
  Feynman path integral for an inverse problem
Brian DeFacio
12:00 PM - 12:30 PM
  Path integrals, momentum representation and stochastic analysis
Jean-Claude Zambrini
12:30 PM - 02:00 PM
02:00 PM - 03:00 PM
  Feynman integrals and non-commutative probability theory
Sarada Rajeev
03:00 PM - 03:30 PM
  Afternoon Tea
04:10 PM - 05:10 PM
  Knot theory and functional integration
Louis Kauffman (University of Illinois at Chicago)
Dec 10, 2002
09:00 AM - 10:00 AM
  Results on the Feynman integral in Feynman's original setting
Gerald Johnson (University of Nebraska)
10:00 AM - 10:30 AM
  Morning Tea
10:30 AM - 11:30 AM
  Feynman's operational calculus via Feynman path integrals and disentangling algebras
Michel Lapidus (University of California, Riverside)
11:30 AM - 02:00 PM
02:00 PM - 03:00 PM
  A general theory of evolutions and path integrals on Banach spaces via the Feynman calculus
Tepper Gill
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:00 PM
  Operator-valued function space integrals
David Storvick
04:00 PM - 04:30 PM
  Fourier-Feynman transforms, convolution products and first variations in function spaces
David Skoug
04:30 PM - 05:00 PM
05:00 PM - 06:00 PM
Dec 11, 2002
09:00 AM - 10:00 AM
  The 2-D Yang-Mills functional integral: Physics applied to geometry
Ambar Sengupta (University of Connecticut)
10:00 AM - 10:30 AM
  Morning Tea
10:30 AM - 11:30 AM
  Rigorous stochastic model representation for the Wilson loop observables in Chern-Simons theory
Atle Hahn
11:30 AM - 02:00 PM
02:00 PM - 03:00 PM
  Path integrals for the 1-D Dirac equation
Brian Jefferies
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Path integrals: Flexible tools
John LaChapelle
04:30 PM - 05:00 PM
  Open problems and discussion
Dec 12, 2002
09:00 AM - 10:00 AM
  An introduction to quantum computing
Umesh Vazirani (University of California, Berkeley)
10:00 AM - 10:30 AM
  Morning Tea
10:30 AM - 11:00 AM
  Functional integration and quantum computing
Louis Kauffman (University of Illinois at Chicago)
11:15 AM - 11:45 AM
  Feynman integrals: Mathematical challenges
Samuel Lomonaco
12:00 PM - 12:30 PM
  Could quantum computing aid functional integration?
David Collins
12:30 PM - 02:30 PM
02:30 PM - 03:00 PM
  Extraction of linear factors in Feynman's operational calculus
Byoung Soo Kim
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:00 PM
  Oscillatory (Feynman) integrals for the Schroedinger equation in a magnetic field
Zdzislaw Brzezniak
04:00 PM - 04:30 PM
  New developments of rigorous Feynman path integrals and application to a stochastic Schroedinger equation
Sonia Mazzucchi