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. |
Contents
Contents | 1 |
Bound State Calculations | 5 |
Algebraic Schrödinger Representation | 47 |
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Aai(x algebraic anticommutators antisymmetrized apply assume auxiliary fields basis vectors boson-fermion bound calculation canonical canonical quantization Chapter commutator composite particle composite particle dynamics composite particle theory consider Cooper pair corresponding covariant formalism cyclic decomposition defined definition derivation Dirac discussion dressed particle dual eigenstates eigenvalue equations energy equation evaluation expressions fermion field equations field operators Fock space functional equation functional space Furthermore given groundstate Hamilton formalism Hamiltonian hard core Hence I₁ interaction invariant k₁ K₂ Krein space means metrical tensor normalordering obtain path integrals permutations physical Poincaré group Proof propagator Proposition quantization quantum field theory quantum numbers quantum theory r₁ relations renormalization representation respect right-hand side Section selfadjoint sgn(p solutions spinor spinorfield Stumpf Stu subfermions substitute summation symmetry t₁ time-ordered products transformation transition matrix elements vacuum expectation values vector bosons wavefunctions yields z₂ αβγδ