Showing papers by "Jean-Pierre Eckmann published in 1976"
TL;DR: In this article, the authors considered the λ(ϕ6−ϕ4) quantum field theory in two space-time dimensions and showed that there is a unique two particle bound state if the coupling constant λ>0 is sufficiently small.
Abstract: We consider the λ(ϕ6−ϕ4) quantum field theory in two space-time dimensions. Using the Bethe-Salpeter equation, we show that there is a unique two particle bound state if the coupling constant λ>0 is sufficiently small. Ifm is the mass of single particles then the bound state mass is given by
$$_B (\lambda ) = 2m\left( {1 - \frac{9}{8}\left( {\frac{\lambda }{{m^2 }}} \right)} \right)^2 + \mathcal{O}\left( {\lambda ^3 } \right).$$
34 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
TL;DR: In this paper, the authors present MASLOV's method at an elementary level, thus making his beautiful ideas available to a larger audience, and restrict themselves to the easy possible case, the harmonic oscillator in one dimension.
Abstract: In his book \"Th6orie des Perturbations et M6thodes Asymptotiques\" V.P.MAsLOV has given an ingenious approximation method which overcomes certain well known difficulties in the classical WKB approach. One of these difficulties is connected with the singularities of the amplitudes of the wave function which appear at turning points of a classical motion. Another arises from the fact that the relative phases of the different contributions to the WKB wave function are obtained from a priori knowledge about its behaviour outside the domain of the classical motion and are therefore not intrinsic. Both these problems are solved in a most natural way in MASLOV'S approach. Unfortunately, his book is not easy to read and often it is difficult to decide whether the assertions are really proved. This paper is an attempt to present MASLOV'S method at an elementary level, thus making his beautiful ideas available to a larger audience. We restrict ourselves to the easiest possible case, the harmonic oscillator in one dimension. This we hope will make the exposition more transparent. It turns out that the necessary techniques to prove the assertions in this easy example are already prototypes for the proofs in the general case. Therefore our limitation to a particular example is only a matter of convenience and not really a simplification of the main problems which occur in the most general situation. Since it is our goal to explore the limit h ~ 0 in quantum mechanics, we begin with a short study of the classical system for our model Hamiltonian
26 citations
01 Jan 1976
TL;DR: This article described results of a paper with the same title done jointly with H. Epstein and J. Frohlich, and reported their results at this conference, but did not describe any of their methods.
Abstract: This talk describes results of a paper with the same title done jointly with H. Epstein and J. Frohlich. Similar work has been done simultaneously and independently by J. Dimock, K. Osterwalder, and R. Seneor, and since they also report at this conference I will not describe any of their methods.
4 citations