DIFFERENTIABLE VECTORS AND SHARP MOMENTUM STATES OF HELICITY REPRESENTATIONS OF THE POINCARE GROUP

Ek, B.; Nagel, B.

doi:10.1063/1.526343

DIFFERENTIABLE VECTORS AND SHARP MOMENTUM STATES OF HELICITY REPRESENTATIONS OF THE POINCARE GROUP

1984

9 pages

Published in:

J.Math.Phys. 25 (1984) 1662-1670

DOI:

10.1063/1.526343

View in:

reference search5 citations

Citations per year

Abstract: (AIP)

This paper discusses some mathematical difficulties in handling sharp momentum eigenvectors for a massless helicity representation of the Poincaré group, related to the non‐nuclearity of the space of differentiable vectors, and to the existence of singularities in the Lorentz group generators. A simple characterization of the nuclear space of differentiable vectors of the extension of the representation to a representation of the conformal group is given in terms of functions on the space R4− {0}. Using a fibration of this space over the forward light cone (in momentum space), the singularity in the generators is shown to be related to the fact that the standard presentation of the helicity representations should be reformulated in terms of nontrivial sections over the light cone. The problem is partly identical with the one encountered in the study of an electron in a magnetic monopole field, the generator singularity taking the place of the Dirac string.

GROUP THEORY: LORENTZ
GROUP THEORY: REPRESENTATION
HELICITY
SPIN
FIELD THEORY: FIBRE BUNDLE
commutation relations
POSTULATED PARTICLE: MAGNETIC MONOPOLE

References(0)

Figures(0)

0 References