# Mathematical Sciences Research Institute

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# Workshop

The Feynman Integral Along with Related Topics and Applications December 09, 2002 - December 12, 2002
 Registration Deadline: December 12, 2002 almost 12 years ago September 09, 2002 about 12 years ago
Organizers Sergio Albeverio, Cecile DeWitt-Morette, Gerald W. Johnson, Louis H. Kauffman, and Michel L. Lapidus (chair)
Speaker(s)

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Description

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.

Funding & Logistics

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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.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates 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 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

## Show Visa/Immigration

Schedule
Dec 09, 2002
Monday
 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) 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 Lunch 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
Tuesday
 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) 11:30 AM - 02:00 PM Lunch 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 Concert 05:00 PM - 06:00 PM Reception
Dec 11, 2002
Wednesday
 09:00 AM - 10:00 AM The 2-D Yang-Mills functional integral: Physics applied to geometry Ambar Sengupta 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 Lunch 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
Thursday
 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 Lunch 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