V. Glaser

Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations

We show that for a wide class of Euclidean scalar field equations, there exist non-trivial solutions, and the non-trivial solution of lowest action is spherically symmetric. This fills a gap in a recent analysis of vacuum decay by one of us.

A proof of the crossing property for two-particle amplitudes in general quantum field theory

In the framework of the ℒ.l.Z. formalism, the crossing property is proved on the mass shell for amplitudes involving two incoming and two outgoing stable particles with arbitrary masses. Any couple of physical regions in the (s, t, u)-plane corresponding to crossed processes are shown to be connected by a certain domain of analyticity. For every negative value oft, the amplitude is analytic in the cuts-plane outside of a large circle.

Some rigorous analyticity properties of the four-point function in momentum space

SummaryGeometrical methods of analytic completion are used to enlarge the primitive domain of analyticity of the four-point function inp-space. The results imply, in particular, analyticity of the scattering amplitude in two variables, on the mass shell, near all physical points, as well as analyticity of partial-wave amplitudes ins near the physical points of the right-hand side cut.RiassuntoSi usano i metodi geometrici di completamento analitico per ampliare il primitivo dominio di analiticità della funzione di quattro punti nello spaziop. I risultati implicano, in particolare, l’analiticità dell’ampiezza di scattering rispetto a due variabili, sul guscio della massa, in prossimità di tutti i punti fisici, ed anche l’analiticità delle ampiezze dell’onda parziale ins presso tutti i punti del taglio del lato destro.

On the connection between analyticity and Lorentz covariance of Wightman functions

We prove a conjecture ofR. Streater [1] on the finite covariance of functions holomorphic in the extended tube which are Laplace transforms of two tempered distributions with supports in the future and past cones. A new, slightly more general proof is given for a theorem of analytic completion of [1].

POLYNOMIAL BEHAVIOUR OF SCATTERING AMPLITUDES AT FIXED MOMENTUM TRANSFER IN THEORIES WITH LOCAL OBSERVABLES.

AbstractIt is shown that, in theories of exactly localized observables, of the type proposed byAraki andHaag, the reaction amplitude for two particles giving two particles is polynomially bounded ins for fixed momentum transfert<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products

On the equivalence of the Euclidean and Wightman formulation of field theory

\int {\varphi (x_1 ,..., x_n ) \phi _1 } (x - x_1 ) ... \phi _n (x - x_n )dx_1 ...dx_n

Study of the Iterations of a Mapping Associated to a Spin Glass Model

ofWightman orJaffe fields.

Some analyticity properties arising from asymptotic completeness in quantum field theory

SummaryThe two-dimensional model of a relativistic theory proposed recently byW. Thirring (1) is solved by displaying the field operator ψ as an explicit functional of the corresponding incoming field. TheS-matrix (without external sources) is found to be of the form,S=exp [iQ1Q2, where Q1,2 are two constants of the motion. TheS-matrix is unitary, but gives rise only to a relative change of phase of the plane waves associated with the colliding particles, all the cross-sections being equal to zero (2). After the renormalization, all the matrix elements of the field operator turn out to be finite analytic functions of the coupling constant. An apparent discrepancy with the results ofThirring (*) is discussed.RiassuntoSi risolve il modello bidimensionale di una teoria relat.ivistica recentemente proposta daW. E. Thirring (1) sviluppando l’operatore di campo ψ come funzionale esplicito del corrispondente campo entrante. Si t.rova che la matriceS (senza sorgenti esterne) è della formaS = exp [iQ1Q2], doveQ12 sono due costanti del moto. La matriceS è unitaria, ma dà luogo solo ad un cambiamento relativo di fase delie onde piane associate alle particelle che collidono, tutte le sezioni d’urto essendo uguali a zero (2) Dopo la rinormalizzazione tutti gli elementi di matrice dell’operatore di campo risultano funzioni analitche, finite della costante di accoppiamento. Si discute un’apparente discrepanza coi risultati diThirring (1).