## The relativistic polaron without cutoffs in two space dimensions |

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### Contents

Chapter IFormalism of Quantum Field Theory | 5 |

Chapter IIA Cutoff Model of the Polaron | 54 |

Chapter IIIOne Particle Rest States | 80 |

2 other sections not shown

### Common terms and phrases

adjoint operator approximate wave factor bilinear form bounded linear operators characteristic function closed operator commute compact set compact subset compact support complex numbers component Consequently continuous function coordinate directions cp(f cutoff functions D(HQ denote dense set dense subset densely defined differentiable direct sum domain dominated convergence electron finite linear combinations fixed Fock space follows free Hamiltonian Fubini's theorem Hausdorff space Hilbert space Holder's inequality HQ(p induction Let f Let g Let h lim H measurable function non-negative integer partial derivatives phonon pointwise polaron positive integer positive number Proof Q.E.D. Corollary Q.E.D. Definition Q.E.D. Lemma real subspace relatively bounded Rn(p satisfies Schwarz's inequality self-adjoint operator sequence spectral projections spectral theorem spectrum strongly integrable suffices to prove sup sup suppose g symmetric term unitary operator V_1W vector W_1V zero total momentum