Abstract
In this chapter different Dirac operators will be defined. The construction of such an operator follows a general pattern: first we construct a vector space of functions having special properties (‘sections’ or ‘fields’). An example of these is the one of Clifford fields. Then a derivation rule (a connection) is defined. Because of the embedding we work with, it is always possible to express this connection in terms of derivation followed by projection onto the space of sections Finally we construct a first order differential operator satisfying some form of Stokes’ equation: this is the Dirac operator.
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© 2002 Springer Science+Business Media New York
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Cnops, J. (2002). Dirac Operators. In: An Introduction to Dirac Operators on Manifolds. Progress in Mathematical Physics, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0065-9_3
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DOI: https://doi.org/10.1007/978-1-4612-0065-9_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6596-2
Online ISBN: 978-1-4612-0065-9
eBook Packages: Springer Book Archive