Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enhanced Binding in Quantum Field Theory   This lecture note consists of three parts. Fundamental facts on Boson Fock
space are introduced in Part I. Ref. 1.and 3. are reviewed in Part II and, Ref.
2. and 4. in Part III.
  In Part I a symplectic structure of a Boson Fock space is studied and a
projective unitary representation of an infinite dimensional symplectic group
through Bogoliubov transformations is constructed.
  In Part II the so-called Pauli-Fierz model (PF model) with the dipole
approximation in non-relativistic quantum electrodynamics is investigated. This
model describes a minimal interaction between a massless quantized radiation
field and a quantum mechanical particle (electron) governed by Schr\"odinger
operator. By applying the Bogoliubov transformation introduced in Part I we
investigate the spectrum of the PF model. First the translation invariant case
is considered and the dressed electron state with a fixed momentum is studied.
Secondly the absence of ground state is proven by extending the
Birman-Schwinger principle. Finally the enhanced binding of a ground state is
discussed and the transition from unbinding to binding is shown.
  In Part III the so-called $N$-body Nelson model is studied. This model
describes a linear interaction between a scalar field and $N$-body quantum
mechanical particles. First the enhanced binding is shown by checking the
so-called stability condition. Secondly the Nelson model with variable
coefficients is discussed, which model can be derived when the Minkowskian
space-time is replaced by a static Riemannian manifold, and the absence of
ground state is proven, if the variable mass decays to zero sufficiently fast.
The strategy is based on a path measure argument.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc