## Composite Particle Dynamics in Quantum Field TheoryEach atomistic theory of matter is based on the idea that agglomerations of their constituents are to be identified with observable objects of physical reality and that in this way the diversity of physical phenomena and reactions can be reduced to the interplay of a few elementary entities. This means theoretically that the formation of observable objects and their reactions have to be derived from the dynamics of their atomistic, i. e. elementary constituents. At present such atomistic theories of matter are formulated by quantum field theories. In view of the above described aim it is thus one of the most important tasks in quantum field theory to derive composite particles as bound states and to explain their dynamics as an effective dynamics induced by the elementary fields. In the development of quantum field theory many attempts have been made to solve this problem. So far, however, these attempts have been unsatisfactory and in this book some comments will be made on what the reasons are and where the difficulties arise. Roughly speaking the latter are closely connected with the idea to describe the effective dynamics of composite particles by means of the dynamics of field operator products. To avoid these difficulties we alternatively developed the method of weak mapping of quantum fields. The presentation of this method and of some applications to current problems is the object of this monography. |

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### Contents

Contents | 1 |

Covariant Quantum Field Dynamics | 21 |

Algebraic Schrddinger Representation | 47 |

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### Common terms and phrases

According algebraic anticommutation antisymmetric apply approximation assume auxiliary fields basis vectors boson-fermion calculation canonical Chapter composite particle composite particle dynamics composite particle theory consider Cooper pair coordinates corresponding covariant formalism decomposition defined definition derivation Dirac discussion dressed fermion dressed particle duals effective dynamics effective theories eigenstates eigenvalue equation energy equation evaluation explicitly expressions field equations field operators Fock space functional equation functional space Furthermore given graviton groundstate Hamilton formalism Hamiltonian Heisenberg Hence hyperplane interaction introduce invariant Krein space means metrical tensor nonabelian normalordering obtain p€Sn path integrals performed permutations physical Poincare polarization cloud Proof propagator Proposition quantization quantum electrodynamics quantum field theory quantum numbers quantum theory relativistic renormalization representation respect Section selfadjoint spinor spinorfield Stumpf Stu subfermions substitute superconductivity superspinor symmetry temporal gauge transformation transition matrix elements two-fermion vacuum expectation values vector bosons wave functions wavefunctions weak mapping theorems yields