EAN: 9789811956775

INFINITE-DIMENSIONAL DIRAC OPERATORS AND SUPERS...

This book explains the mathematical structures of supersymmetric quantum field theory (SQFT)
from the viewpoints of functional and infinite-dimensional analysis. The main mathematical
objects are infinite-dimensional Dirac operators on the abstract Boson-Fermion Fock space. The
target audience consists of graduate students and researchers who are interested in
mathematical analysis of quantum fields  including supersymmetric ones  and
infinite-dimensional analysis. The major topics are the clarification of general mathematical
structures that some models in the SQFT have in common  and the mathematically rigorous
analysis of them. The importance and the relevance of the subject are that in physics
literature  supersymmetric quantum field models are only formally (heuristically) considered
and hence may be ill-defined mathematically. From a mathematical point of view  however  they
suggest new aspects related to infinite-dimensional geometry and analysis. Therefore  it is
important to show the mathematical existence of such models first and then study them in
detail. The book shows that the theory of the abstract Boson-Fermion Fock space serves this
purpose. The analysis developed in the book also provides a good example of
infinite-dimensional analysis from the functional analysis point of view  including a theory of
infinite-dimensional Dirac operators and Laplacians.

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