相关论文: Infrared Catastrophe for Nelson's Model

We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with variable coefficients arise when one replaces in the usual…

We consider the Nelson model on some static space-times and investigate the problem of absence of a ground state. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a…

For the massless Nelson model we provide detailed information about the dependence of the normalized ground states $\check{\psi}_{P,\sigma}$ of the fiber single-electron Hamiltonians $H_{P,\sigma}$ on the total momentum $P$ and the infrared…

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field…

The massless Nelson model describes non-relativistic, spinless quantum particles interacting with a relativistic, massless, scalar quantum field. The interaction is linear in the field. We analyze the one particle sector. First, we…

We prove the existence, uniqueness, and strict positivity of ground states of the possibly massless renormalized Nelson operator under an infrared regularity condition and for Kato decomposable electrostatic potentials fulfilling a binding…

We calculate the tunneling density of states of a two-dimensional interacting electron gas in a quantizing magnetic field. We show that the observed pseudogap in the density of states can be understood as the result of an infrared…

We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently…

We show asymptotic completeness of two-body scattering for a class of translation invariant models describing a single quantum particle (the electron) linearly coupled to a massive scalar field (bosons). Our proof is based on a recently…

In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form…

The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock…

The existence of a ground state of the Nelson Hamiltonian with a perturbation is considered. The self-adjointness of the Hamiltonian and the existence of a ground state are proven for arbitrary values of coupling constants.

We study properties of the ground state of the Nelson model through functional integration. We obtain bounds on the average and the variance of the Bose field both in position and momentum space, on the distribution of the number of bosons,…

We construct two-electron scattering states and verify their tensor product structure in the infrared-regular massless Nelson model. The proof follows the lines of Haag-Ruelle scattering theory: Scattering state approximants are defined…

Abstract interior-boundary conditions (IBC's) allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in Quantum Field Theory. The method was recently applied to…

The translation invariant model in quantum field theory is considered by functional integrations. Ultraviolet renormalization of the translation invariant Nelson model with a fixed total momentum is proven by functional integrations. As a…

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…

We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. In contrast, for…

Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial…

Positive definiteness of a Hamiltonian expanded about an equilibrium point provides only a necessary condition for stability, a criterion known as Dirichlet's theorem. The reason that this criterion is not necessary for stability is because…