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Ground States for translationally invariant Pauli-Fierz Models at zero Momentum

David Hasler, Oliver Siebert

Abstract

We consider the translationally invariant Pauli-Fierz model describing a charged particle interacting with the electromagnetic field. We show under natural assumptions that the fiber Hamiltonian at zero momentum has a ground state.

Ground States for translationally invariant Pauli-Fierz Models at zero Momentum

Abstract

We consider the translationally invariant Pauli-Fierz model describing a charged particle interacting with the electromagnetic field. We show under natural assumptions that the fiber Hamiltonian at zero momentum has a ground state.

Paper Structure

This paper contains 8 sections, 25 theorems, 129 equations.

Table of Contents

  1. Introduction
  2. Model and Statement of Results
  3. Proof of Results
  4. Ground State Properties for massive Photons
  5. Infrared Bounds
  6. Existence of the Ground State
  7. Self-adjointness
  8. Ground State for positive Photon Mass

Key Result

Theorem 1

Suppose Hypothesis A holds, and let $e \in {\mathord{\mathbb R}}$. If there exists an $m_0 > 0$ such that for all $m \in (0,m_0)$ the energy inequality eq:eineq holds, then the operator $H(0)$ has a ground state.

Theorems & Definitions (44)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Remark 1
  • Proposition 5
  • proof
  • Lemma 6
  • proof
  • Proposition 7
  • ...and 34 more