• Corpus ID: 246035601

The Euclidean $\phi^4_2$ theory as a limit of an interacting Bose gas

  title={The Euclidean \$\phi^4\_2\$ theory as a limit of an interacting Bose gas},
  author={Jurg Frohlich and Antti Knowles and Benjamin Schlein and Vedran Sohinger},
We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the interaction becomes small. The field theory is supported on distributions of negative regularity, which requires a renormalization by divergent mass and energy counterterms. We obtain convergence of the relative partition function and uniform convergence of the… 



The mean-field limit of quantum Bose gases at positive temperature

We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schr\"odinger equation in the mean-field limit, where the density of the

Classical field theory limit of many-body quantum Gibbs states in 2D and 3D

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the

Classical field theory limit of 2D many-body quantum Gibbs states

Nonlinear Gibbs measures play an important role in many areas of mathematics, including nonlinear dispersive equations with random initial data and stochastic partial differential equations. In

Euclidean Quantum Field Theory. I: Equations For A Scalar Model

The analytic continuations to imaginary time of the Green's functions of local quantum field theory define Euclidean Green's functions. Use of the proper‐time method allows to represent these

Marginal triviality of the scaling limits of critical 4D Ising and 𝜑44 models

We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar

A Microscopic Derivation of Gibbs Measures for Nonlinear Schrödinger Equations with Unbounded Interaction Potentials

  • V. Sohinger
  • Mathematics
    International Mathematics Research Notices
  • 2021
We study the derivation of the Gibbs measure for the nonlinear Schrödinger (NLS) equation from many-body quantum thermal states in the mean-field limit. In this paper, we consider the nonlocal NLS

Derivation of nonlinear Gibbs measures from many-body quantum mechanics

We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the

The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas

We rigorously establish the existence of a Kosterlitz-Thouless transition in the rotator, the Villain, the solid-on-solid, and the ℤn models, forn large enough, and in the Coulomb lattice gas, in two

Exponential Relaxation to Equilibrium for a One-Dimensional Focusing Non-Linear Schrödinger Equation with Noise

We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear