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“Canonical” representations of the inhomogeneous lorentz group
196
ABSTRACTS
OF
PAPERS
TO
where all2 and ~2 are s-wave pion-nucleon and N, respectively. (iv) Under certain approximations discussed magnetic moment I** is given by
to be compared land.
with
the value
Jo* =
(1.28
APPEAR
scattering
f
IN
FUTURE
lengths
ISSUES
corresponding
in the text,
we show
0.02)?&&,
obtained
that
by
the N*N
Dalitz
to isospin
x
transition
and Suther-
Radiative Transfer in a Free-Electron Atmosphere. C. E. SIEWERT AND S. K. FRALEY. Department of Nuclear Engineering, North Carolina State University, Raleigh, North Carolina. The equations of radiative transfer for an electron-scattering atmosphere, as developed by Chandrasekhar, are solved using Case’s method of singular eigensolutions. The eigenfunctions of the set of coupled transport equations have been found. There are two discrete eigenvectors and two linearly independent, degenerate, singular, continuum eigensolutions. These eigenvectors are shown to form a complete basis set for the expansion of arbitrary two-component vectors defined on the half-range. In addition, all of the necessary adjoint functions have been developed so that all expansion coefficients can be obtained by taking scalar products. As an example of the met,hod, the Milne problem is solved and explicit results are obtained for the two-components of the polarized radiation field at any oplicadepth in the stellar medium. “Canonical” Representations of the Inhomogeneous Lore&z Group. G. LUGARINI AND M. PAURI. Instituto di Fisica dell’Universita, Parma, Italy. A systematic characterization is given of the basic unitary representations of the Inhomogeneous Lorentz Group which are of interest in classical mechanics. The study is carried out on the ground of a representation theory for classical mechanics previously proposed. Accordingly, the irreducible representations, in the “classical” Hilbert space of Koopmanvon Newmann, which are the proper unitary counterpart of the canonical (phase-space) realizations of the Poincare group in the neighborhood of t,he identity (“canonical” representations), are classified and explicitly derived. The irreducible “canonical” representations which can be taken into account from a physical point of view are essentially of three kinds: representations corresponding to free particles of finite rest-mass and arbitrarily fixed spin; representations corresponding to particles of zero rest-mass and pure, arbitrarily fixed, heliticy and, finally, other representat,ions describing systems of zero rest-mass with a “spin” which depends on the Lorentz frame and can assume any positive real value. Except possibly for the photon, the last two classes can hardly be connected with realistic classical models. The related relativistic Liottville equations of motion are deduced.
ABSTRACTS
OF
PAPERS
TO
where all2 and ~2 are s-wave pion-nucleon and N, respectively. (iv) Under certain approximations discussed magnetic moment I** is given by
to be compared land.
with
the value
Jo* =
(1.28
APPEAR
scattering
f
IN
FUTURE
lengths
ISSUES
corresponding
in the text,
we show
0.02)?&&,
obtained
that
by
the N*N
Dalitz
to isospin
x
transition
and Suther-
Radiative Transfer in a Free-Electron Atmosphere. C. E. SIEWERT AND S. K. FRALEY. Department of Nuclear Engineering, North Carolina State University, Raleigh, North Carolina. The equations of radiative transfer for an electron-scattering atmosphere, as developed by Chandrasekhar, are solved using Case’s method of singular eigensolutions. The eigenfunctions of the set of coupled transport equations have been found. There are two discrete eigenvectors and two linearly independent, degenerate, singular, continuum eigensolutions. These eigenvectors are shown to form a complete basis set for the expansion of arbitrary two-component vectors defined on the half-range. In addition, all of the necessary adjoint functions have been developed so that all expansion coefficients can be obtained by taking scalar products. As an example of the met,hod, the Milne problem is solved and explicit results are obtained for the two-components of the polarized radiation field at any oplicadepth in the stellar medium. “Canonical” Representations of the Inhomogeneous Lore&z Group. G. LUGARINI AND M. PAURI. Instituto di Fisica dell’Universita, Parma, Italy. A systematic characterization is given of the basic unitary representations of the Inhomogeneous Lorentz Group which are of interest in classical mechanics. The study is carried out on the ground of a representation theory for classical mechanics previously proposed. Accordingly, the irreducible representations, in the “classical” Hilbert space of Koopmanvon Newmann, which are the proper unitary counterpart of the canonical (phase-space) realizations of the Poincare group in the neighborhood of t,he identity (“canonical” representations), are classified and explicitly derived. The irreducible “canonical” representations which can be taken into account from a physical point of view are essentially of three kinds: representations corresponding to free particles of finite rest-mass and arbitrarily fixed spin; representations corresponding to particles of zero rest-mass and pure, arbitrarily fixed, heliticy and, finally, other representat,ions describing systems of zero rest-mass with a “spin” which depends on the Lorentz frame and can assume any positive real value. Except possibly for the photon, the last two classes can hardly be connected with realistic classical models. The related relativistic Liottville equations of motion are deduced.