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Symmetric distributions of bound fermions
ANNALS
OF PHYSICS:
83, 242-244 (1974)
Abstracts
of Papers
to Appear
in Future
Issues
on Space-Time Hyperboloids. CHARLES M. SOMMERFIELD. Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520. A quantization scheme which specifies commutation relations on space-time hyperboloids is examined and shown to lead to a Fock space different from the usual one. Nevertheless, the theories are shown to be physically equivalent if properly interpreted. Quatttizatiott
Disfriburions oJ’ Bound Fermions. KURT JUST. Department of Physics, University of Arizona, Tucson, Arizona 8572 1. Relativistic models of hadrons composed of the simplest kind of Fermi quarks will be described in subsequent papers by symmetric wave functions S, which vanish when all the relative positions of the constituents are spacelike. These S are here found highly preferable, not in spite of, but thanks to the usual connection of spin and statistics. The principles of the new models are explained in comparison with other quark and parton models. If needed at all, the BetheSalpeter amplitude Tof a bound state can be obtained from its symmetric distribution S by a “dispersion” integral. An extension to three constituents will be given later. It is precisely because S vanishes for spacelike internal separations that practical estimates for strongly bound states will more readily employ that symmetric distribution than the time ordered T. Field theory and its description of bound states, as well as properties and interactions of hadrons, are invoked for completeness and the benefit of specialists. Only elementary notions from such topics, however, are needed for the main conclusion. It says that the simplest Fermi quarks (without any “hidden” quantum number) offer the best explanation for the widely accepted symmetry of their wave functions in baryons. The failure to observe quarks and also their oscillator shaped interaction within hadrons will later be connected with the same simplicity and a vanishing mass of “bare” quarks. Symmetric
in Angular Correlations as an bzterfererwe Pllenomenotz. H. J. LEISI. Laboratory for High Energy Physics, Swiss Federal Institute of Technology Zurich, c/o SIN, 5234 Villigen, Switzerland. A complete derivation of the new formulation of the theory of perturbed angular correlations of time-independent interactions [I] is presented. Gamma-gamma directional correlation experiments are explicitly considered. The directional correlation functions for time-differential and time-integrated experiments are derived, including expressions for the general class of isotropic systems (powder sources). The formula for the interference amplitude which depends on the nuclear parameters and on the eigenfunctions of the interaction Hamiltonian is derived for an arbitrary (time-independent) interaction. Properties of the interference terms that follow from symmetries of the interaction Hamiltonian are discussed. A general proof of the theorem concerning the interference of time reversed states is given. The new approach is demonstrated by considering three angular correlation problems explicitly, namely the coupling between the nuclear magnetic moment and a magnetic field, the (axially-symmetric) quadrupole interaction in a crystal and the hyperfine interaction in a free atom in the Zeeman region. The results (some of which are well known) are derived with a particular emphasis on the close relationship between the angular correlation function and the level structure of the system in the intermediate state. The results are also relevant to a number of recent experiments which clearly demonstrate the quantum-mechanical interference nature of the angular correlation process. These experiments are briefly discussed. An extension of the present theory in order to include time-dependent perturbations is suggested. 242 Perturbations
Copyright All rights
Q 1974 by Academic Press, Inc. of reproduction in any form reserved.
OF PHYSICS:
83, 242-244 (1974)
Abstracts
of Papers
to Appear
in Future
Issues
on Space-Time Hyperboloids. CHARLES M. SOMMERFIELD. Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520. A quantization scheme which specifies commutation relations on space-time hyperboloids is examined and shown to lead to a Fock space different from the usual one. Nevertheless, the theories are shown to be physically equivalent if properly interpreted. Quatttizatiott
Disfriburions oJ’ Bound Fermions. KURT JUST. Department of Physics, University of Arizona, Tucson, Arizona 8572 1. Relativistic models of hadrons composed of the simplest kind of Fermi quarks will be described in subsequent papers by symmetric wave functions S, which vanish when all the relative positions of the constituents are spacelike. These S are here found highly preferable, not in spite of, but thanks to the usual connection of spin and statistics. The principles of the new models are explained in comparison with other quark and parton models. If needed at all, the BetheSalpeter amplitude Tof a bound state can be obtained from its symmetric distribution S by a “dispersion” integral. An extension to three constituents will be given later. It is precisely because S vanishes for spacelike internal separations that practical estimates for strongly bound states will more readily employ that symmetric distribution than the time ordered T. Field theory and its description of bound states, as well as properties and interactions of hadrons, are invoked for completeness and the benefit of specialists. Only elementary notions from such topics, however, are needed for the main conclusion. It says that the simplest Fermi quarks (without any “hidden” quantum number) offer the best explanation for the widely accepted symmetry of their wave functions in baryons. The failure to observe quarks and also their oscillator shaped interaction within hadrons will later be connected with the same simplicity and a vanishing mass of “bare” quarks. Symmetric
in Angular Correlations as an bzterfererwe Pllenomenotz. H. J. LEISI. Laboratory for High Energy Physics, Swiss Federal Institute of Technology Zurich, c/o SIN, 5234 Villigen, Switzerland. A complete derivation of the new formulation of the theory of perturbed angular correlations of time-independent interactions [I] is presented. Gamma-gamma directional correlation experiments are explicitly considered. The directional correlation functions for time-differential and time-integrated experiments are derived, including expressions for the general class of isotropic systems (powder sources). The formula for the interference amplitude which depends on the nuclear parameters and on the eigenfunctions of the interaction Hamiltonian is derived for an arbitrary (time-independent) interaction. Properties of the interference terms that follow from symmetries of the interaction Hamiltonian are discussed. A general proof of the theorem concerning the interference of time reversed states is given. The new approach is demonstrated by considering three angular correlation problems explicitly, namely the coupling between the nuclear magnetic moment and a magnetic field, the (axially-symmetric) quadrupole interaction in a crystal and the hyperfine interaction in a free atom in the Zeeman region. The results (some of which are well known) are derived with a particular emphasis on the close relationship between the angular correlation function and the level structure of the system in the intermediate state. The results are also relevant to a number of recent experiments which clearly demonstrate the quantum-mechanical interference nature of the angular correlation process. These experiments are briefly discussed. An extension of the present theory in order to include time-dependent perturbations is suggested. 242 Perturbations
Copyright All rights
Q 1974 by Academic Press, Inc. of reproduction in any form reserved.