Showing papers by "Jürg Fröhlich published in 1976"
TL;DR: In this article, it was shown that phase transitions occur in (φ·φ) 3 2 quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions.
Abstract: We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ) 3 2 quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function ink space is bounded by 0(k−2). When applicable, our results can be fairly accurate numerically. For example, our lower bounds on the critical temperature in the three dimensional Ising (resp. classical Heisenberg) model agrees with that obtained by high temperature expansions to within 14% (resp. a factor of 9%).
484 citations
TL;DR: In this article, the canonical and grand canonical partition function in a finite volume and the existence of the thermodynamic limit for the pressure of two component classical and quantum systems of particles with charge ±e interacting via two body Yukawa forces were established.
Abstract: We estimate the canonical and grand canonical partition function in a finite volume and prove stability and existence of the thermodynamic limit for the pressure of two component classical and quantum systems of particles with charge ±e interacting via two body Yukawa — or Coulomb forces. In the case of Coulomb forces we require neutrality. For the classical system in two dimensions there exists a critical temperatureTc at and below which the system collapses. For the classical Yukawa system the correlation functions exist for arbitrary fugacity and the general structure of the pure phases can be analyzed completely.
155 citations
Journal Article•
122 citations
TL;DR: In this paper, a rigorous construction of new superselection selectors for the quantum sine-Gordon equation and the (φ·φ)2-quantum field models with explicitly broken isospin symmetry in two space-time dimensions is presented.
Abstract: A rigorous construction of new super-selection selectors — so-called “soliton-sectors” — for the quantum “sine-Gordon” equation and the (φ·φ)2-quantum field models with explicitly broken isospin symmetry in two space-time dimensions is presented These sectors are eigenspaces of the chargeQ≡∫dx(grad φ)(x) with non-zero eigenvalue The scattering theory for quantum solitons is briefly discussed and shown to have consequences for the physics in the vacuum sector A general theory is developed which explains why soliton-sectors may exist for theories in two but not in four space-time dimensions except possibly for non-abelian Yang-Mills theories
115 citations
46 citations
Journal Article•
TL;DR: In weakly coupled P(C)2 theories, perturbation theory in the coupling constant is asymptotic to the S-matrix elements and scattering is non-trivial.
Abstract: In weakly coupled P(C)2 theories, perturbation theory in the coupling constant is asymptotic to the S-matrix elements and scattering is non-trivial. This is derived from regularity properties of the Schwinger functions and a new connection between Schwinger and generalized time ordered functions. PART I SCATTERING IN WEAKLY COUPLED P(I»2 MODELS. PROPERTIES OF THE MODELS AND MAIN RESULTS !
32 citations
01 Jan 1976
TL;DR: In this paper, the authors discuss the existence of relativistic quantum fields and their detailed properties, eg their non-triviality, (in the sense that the scattering matrix is different from the identity [EEF, OSe]).
Abstract: A warning and a reflection: The material I propose to cover in these four lectures is quite large, and ideas from different fields in mathematical physics must be combined Therefore not all the details will be explained I have tried to select proofs for presentation according to their technical simplicity and elegance This should not mislead you to believe that mathematical physics is a simple thing Some of the most outstanding and admirable recent results of, say, constructive quantum field theory (eg [GJ1] [GRS] [GJS1] [OS]; see also [CQFT]) require an enormous amount of sophisticated and hard analysis These results concern the existence of relativistic quantum fields and their detailed properties, eg their non-triviality, (in the sense that the scattering matrix is different from the identity [EEF, OSe]) The fact that the proofs of many of these results are very hard and intricate may seem or be unpleasant
27 citations
01 Jan 1976
TL;DR: The main emphasis of the "International School of Mathematical Physics, 1975" at Erice was clearly on renormalized perturbation theory in the framework of renormalizable quantum field theories which, one hopes, may be relevant for the physics (not only the mathematics) of quantized fields and elementary particles as discussed by the authors.
Abstract: First a warning: The main emphasis of the “International School of Mathematical Physics, 1975” at Erice was clearly on renormalized perturbation theory in the framework of renormalizable quantum field theories which, one hopes, may be relevant for the physics (not only the mathematics) of quantized fields and elementary particles Participants of this school wanted to learn something non-trivial about: ultraviolet renormalization, infrared power counting, the strong adiabatic limit (ie the construction of the scattering matrix), composite fields, Yang-Mills theories, etc In my lectures, however, I study mainly the construction and the detailed properties of a new model of a self-interacting, relativistic scalar Bose field in two space- time dimensions: the quantum sine-Gordon equation (≡ s-G theory)
25 citations
TL;DR: In this paper, it was shown that a Symanzik-nelson positive quantum field theory has a unique decomposition into pure phases which preserves Symanik-Nelson positivity and Poincare covariance.
25 citations