Mathematical Sciences: Analysis of Fermion Fields
{'Code': '03040103', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
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Professor Leonard Gross is one of the leading researchers in               mathematical physics.  He has made major contributions to                       analysis on Hilbert space, probability theory, logarithmic                      Sobolev inequalities, and quantum field theory.  Of highest                     priority in the current proposal is the construction of quantized               Yang-Mills fields.  He hopes to combine his previous work on                    abelian gauge goups with his previous work on nonabelian path                   dependent field strengths and with techniques from stochastic                   differential equations to obtain compactness of Euclidean                       measures.  Second, Professor Gross plans to seek a Euclidean                    extension of his earlier work on Clifford algebra                               hypercontractivity for Fermions.  Such an extension is expected                 to be closely related to the Osterwalder-Schrader formulation of                Euclidean quantum field theory,  Third, Professor Gross plans to                explore the existence of logarithmic Sobolev inequalities on                    noncompact Lie groups and on hyperbolic n-space via the method of               central limit type theorems on groups.
{'FirstName': 'Leonard', 'LastName': 'Gross', 'EmailAddress': 'gross@math.cornell.edu', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Cornell University', 'CityName': 'Ithaca', 'ZipCode': '148502820', 'PhoneNumber': '6072555014', 'StreetAddress': '373 Pine Tree Road', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY'}
{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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