The Ground State Energy of The Massless Spin-Boson Model

Abstract

We provide an explicit combinatorial expansion for the ground state energy of the massless spin-Boson model as a power series in the coupling parameter. Our method uses the technique of cluster expansion in constructive quantum field theory and takes as a starting point the functional integral representation and its reduction to an Ising model on the real line with long range interactions. We prove the analyticity of our expansion and provide an explicit lower bound on the radius of convergence. We do not need multiscale nor renormalization group analysis. A connection to the loop-erased random walk is indicated.

32 pages, 4 figures, a remark and references added, typos corrected, minor computational errors corrected

References in corpus (2)

• Cluster expansion for abstract polymer models. New bounds from an old approach
• Constructive ${\varphi }^4$ field theory without tears

Cited by in corpus (10)

• Analyticity of The Ground State Energy For Massless Nelson Models
• Approach to ground state and time-independent photon bound for massless spin-boson models
• On Existence of Ground States in the Spin Boson Model
• On Asymptotic Expansions in Spin Boson Models
• Nondegeneracy of the Ground State for Nonrelativistic Lee Model
• Spectral analysis of the spin-boson Hamiltonian with two photons for arbitrary coupling
• Correlation Bound for a One-Dimensional Continuous Long-Range Ising Model
• FKN Formula and Ground State Energy for the Spin Boson Model with External Magnetic Field
• Differential Equations of Quantum Mechanics
• Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation