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.

/pdf/a-proof-of-the-crossing-property-for-two-particle-amplitudes-2f0btd4bo8.pdf

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

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].

/pdf/on-the-connection-between-analyticity-and-lorentz-covariance-4mlxailkcp.pdf

On the connection between analyticity and lorentz covariance of wightman functions

Axial Vector Nuclear Sum Rules and Exchange Effects

Although the spin is regarded as a fundamental property of the electron, there is no universally accepted spin operator within the framework of relativistic quantum mechanics. We investigate the properties of different proposals for a relativistic spin operator. It is shown that most candidates are lacking essential features of proper angular momentum operators, leading to spurious zitterbewegung (quivering motion) or violation of the angular momentum algebra. Only the Foldy–Wouthuysen operator and the Pryce operator qualify as proper relativistic spin operators. We demonstrate that ground states of highly charged hydrogen-like ions can be utilized to identify a legitimate relativistic spin operator experimentally.

https://iopscience.iop.org/article/10.1088/1367-2630/16/4/043012/pdf

What is the relativistic spin operator

The main (old and new) results about analyticity properties of two-body transition amplitudes deducible from general local field theory are reviewed. Most of the proofs are included as well as a short chapter on applications.

D. Keefe

Papers

Relations de Dispersion et Particules élémentaires