Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin particles and get (in certain cases) formal solutions of the Dirac equation.
REFERENCES
1.
P.
Podleś
and S. L.
Woronowicz
, “On the classification of quantum Poincaré groups
,” Commun. Math. Phys.
178
, 61
–82
(1996
).2.
P.
Podleś
, “Solutions of Klein-Gordon and Dirac equations on quantum Minkowski spaces
,” Commun. Math. Phys.
181
, 569
–585
(1996
).3.
P.
Podleś
and S. L.
Woronowicz
, “Quantum deformation of Lorentz group
,” Commun. Math. Phys.
130
, 381
–431
(1990
).4.
U.
Carow-Watamura
, M.
Schlieker
, M.
Scholl
and S.
Watamura
, “Tensor representation of the quantum group and quantum Minkowski space
,” Z. Phys. C
48
, 159
–165
(1990
);5.
X.-C.
Song
, “Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation
,” Z. Phys. C
55
, 417
–422
(1992
).6.
A. Schirrmacher, “Quantum groups, quantum spacetime, and Dirac equation,” in Low-Dimensional Topology and Quantum Field Theory, edited by H. Osborn (Plenum, New York, 1993), pp. 221–230.
7.
J. A.
de Azcárraga
, P. P.
Kulish
, and F.
Rodenas
, “Quantum groups and deformed special relativity
,” Fortschr. Phys.
44
, 1
–40
(1996
).8.
P. Podleś, Talk “Dirac equation and gamma matrices for quantum Minkowski spaces,” 5th International colloquium “Quantum groups and integrable systems,” Prague, 20–22 June 1996.
9.
J. A. de Azcárraga, P. P. Kulish, and F. Rodenas, “Twisted h-spacetimes and invariant equations,” q-alg/9702026, to appear in Z. Phys. C (1997).
10.
S. L.
Woronowicz
and S.
Zakrzewski
, “Quantum deformations of the Lorentz group. The Hopf *-algebra level
,” Comput. Math.
90
, 211
–243
(1994
).11.
M.
Chaichian
and A. P.
Demichev
, “Quantum Poincaré group
,” Phys. Lett. B
304
, 220
–224
(1993
).12.
N. Yu.
Reshetikhin
, L. A.
Takhtadzyan
, and L. D.
Faddeev
, “Quantization of Lie groups and Lie algebras
,” Leningrad Math. J.
1
(1
), 193
–225
(1990
)N. Yu.
Reshetikhin
, L. A.
Takhtadzyan
, and L. D.
Faddeev
, [[Alg. anal.
1
(1
), 178
–206
(1989
)].13.
P.
Podleś
and S. L.
Woronowicz
, “On the structure of inhomogeneous quantum groups
,” hep-th/9412058,Commun. Math. Phys.
185
, 325
–358
(1997
).
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1997
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