U.S.-Swiss Cooperative Research in Index Theory and InfiniteDimensional Analysis (Mathematical Physics)
{'Code': '01090000', 'Directorate': {'Abbreviation': 'O/D', 'LongName': 'Office Of The Director'}, 'Division': {'Abbreviation': 'OISE', 'LongName': 'Office Of Internatl Science &Engineering'}}
{'SignBlockName': 'Christine French', 'PO_EMAI': None, 'PO_PHON': None}
This award supports several short term research visits by Arthur                Jaffe and others of Harvard University to the Swiss Federal                     Institute of Technology (ETH) to collaborate in mathematical physics            research with Konrad Osterwalder and others.  The general topic of              the two groups' mutual interest is the geometry of supersymmetric               quantum field models.  The mathematical framework for these problems            is analysis on an infinite dimensional space.  More specifically, a             suitable Hilbert space equipped with a grading gives rise to an                 appropriate decomposition of the Hamiltonian operator H for the                 system as the square of a self adjoint operator Q.  These operators             give rise to an index, which is shown to have good properties such              as homotopy invariance, and relate to a Dirac operator on a finite              dimensional manifold.  The researchers now propose to examine                   several mathematical structures arising from their previous work,               intending to develop an index theory applicable to more generalized             phenomena.  Ultimately, these structures should give further insight            into string theory as well as into other field theories such as the             Wightman field theories.                                                                                                                                        The mathematical research proposed is the first set of existence                theorems and index results for a Dirac operator which couples an                infinite number of degrees of freedom in a non-trivial way.  There              has been a long history of informal collaboration between the                   Harvard and ETH groups which has produced a number of significant               insights in this area.  Funding for a regular schedule of exchange              visits will intensify their collaboration and increase the momentum             and productivity of their research.
{'FirstName': 'Arthur', 'LastName': 'Jaffe', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Arthur M Jaffe', 'EmailAddress': 'Arthur_Jaffe@harvard.edu', 'NSF_ID': '000147847', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Harvard University', 'CityName': 'CAMBRIDGE', 'ZipCode': '021385366', 'PhoneNumber': '6174955501', 'StreetAddress': '1033 MASSACHUSETTS AVE STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MA05', 'ORG_UEI_NUM': 'LN53LCFJFL45', 'ORG_LGL_BUS_NAME': 'PRESIDENT AND FELLOWS OF HARVARD COLLEGE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '5950', 'Text': 'SWITZERLAND'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8722044.xml'}