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.
REFERENCES
1.
H.
Weyl
, The Thoery of Groups and Quantum Mechanics
(Courier Dover Publications
, New York
, 1950
).2.
P. E.
Wigner
, Ann. Math.
40
(1
), 149
(1939
).3.
V.
Bargmann
, Ann. Math.
59
, 1
(1954
).4.
P. E.
Wigner
, Group Theory and Its Application to the Quantum Theory of Atomic Spectra
(Academic
, New York
, 1959
).5.
6.
7.
V.
Bargmann
, J. Math. Phys.
5
(7
), 862
(1964
).8.
G. C.
Hegerfeldt
, K.
Kraus
, and E. P.
Wigner
, J. Math. Phys.
9
(12
), 2029
(1968
).9.
10.
S. K.
Bose
, J. Math. Phys.
36
, 875
(1995
).11.
H.-D.
Doebner
and H.-J.
Mann
, J. Math. Phys.
36
, 3210
(1995
).12.
D. R.
Grigore
, J. Math. Phys.
37
, 460
(1996
).13.
J.
Wawrzycki
, Commun. Math Phys.
250
, 215
(2004
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.
