An extended Galilei group and its application

Erdal İnönü, E. P. Wigner

Erdal İnönü, Eugene Paul Wigner

Christian Duval, P. A. Horváthy

A. Loinger

K. Kraus, H -G Stark

Some quasi-free irreducible representations of the CAR algebra of a non-relativistic free Fermi field are constructed, which are covariant under certain subgroups of the extended Galilei group. The construction of fully covariant (but reducible) representations as direct integrals of partially covariant ones is described. This method is also applicable to arbitrary C*-algebras and other covariance groups.

G. Filippelli

In 1995, Doebner and Mann introduced an approach to the ray representations of the Galilei group in (1 + 1)-dimensions, giving rise to quantum generators with an explicit dependence on time. Recently (2004), Wawrzycki proposed a generalization of Bargmann's theory: in his paper, he introduce phase exponents that are explicitely dependent by 4-space point. In order to find applications of such generalization, we extend the approach of Doebner and Mann to higher dimensions: as a result, we determine the generators of the ray representation in (2 + 1) and (3 + 1) dimensions. The differences of the outcoming formal apparatus with respect to the smaller dimension case are established.