Letters in Mathematical Physics

, Volume 97, Issue 2, pp 165–183 | Cite as

A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles



In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical system by a collection of Dirac states, including the states of the Dirac sea. Formulating the interaction by an action principle for the fermionic projector, we obtain a consistent description of interacting quantum fields which reproduces the results of perturbative quantum field theory. We find a new mechanism for the generation of boson masses and obtain small corrections to the field equations which violate causality.

Mathematics Subject Classification (2010)

81-02 81T15 81T27 


Relativistic quantum theory Dirac sea fermionic projector 


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Copyright information

© Springer 2011

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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