The properties of linear equations on braided linear spaces are investigated and conservation laws for them are derived. The conserved currents are given in the explicit form. The procedure is then applied to scalar wave equations on a quantum plane and on q-Minkowski space.
REFERENCES
1.
Y. Takahashi, An Introduction to Field Quantization (Pergamon, Oxford, 1969).
2.
M.
Klimek
, “Extension of q-deformed analysis and q-deformed models of classical mechanics
,” J. Phys. A
26
, 955
–967
(1993
).3.
M.
Klimek
, “The conservation laws for deformed classical models
,” Czech. J. Phys.
44
, 1049
–1057
(1994
).4.
M.
Klimek
, “The conservation laws and integrals of motion for a certain class of equations in discrete models
,” J. Phys. A
29
, 1747
–1758
(1996
).5.
M.
Klimek
, “Conservation laws for linear equations of motion on quantum Minkowski spaces
,” Commun. Math. Phys.
192
, 29
–45
(1998
).6.
M. Klimek, “The symmetry algebra and conserved currents for Klein-Gordon equation on quantum Minkowski space,” in Quantum Groups and Quantum Spaces, Banach Center Publications, edited by R. Budzyński, W. Pusz, and S. Zakrzewski, Warszawa: Institute of Math., Polish Acad. Sci., Warszawa 1997, Vol. 40.
7.
P.
Podleś
and S. L.
Woronowicz
, “On the structure of inhomogeneous quantum groups
,” Commun. Math. Phys.
185
, 325
–358
(1997
).8.
P.
Podleś
and S. L.
Woronowicz
, “On the classification of quantum Poincaré groups
,” Commun. Math. Phys.
178
, 61
–82
(1996
).9.
P.
Podleś
and S. L.
Woronowicz
, “Quantum deformation of Lorentz group
,” Commun. Math. Phys.
130
, 381
–431
(1990
).10.
P.
Podleś
, “Solutions of Klein–Gordon and Dirac equations on quantum Minkowski spaces
,” Commun. Math. Phys.
181
, 569
–585
(1996
).11.
S. Majid, “Introduction to braided geometry and q-Minkowski space” in Quantum Groups and their Applications, Proceedings of the International School of Physics “Enrico Fermi” Varenna, edited by L. Castellani and J. Wess, 1994.
12.
U.
Meyer
, “Wave equations on q-Minkowski space
,” Commun. Math. Phys.
174
, 457
–475
(1996
).13.
M.
Pillin
, “q-deformed relativistic wave equations
,” J. Math. Phys.
35
, 2804
–2817
(1994
).14.
S.
Majid
, “Free braided differential calculus, braided binomial theorem and the braided exponential map
,” J. Math. Phys.
34
, 4843
–4856
(1993
).15.
S.
Majid
, “Braided momentum in the q-Poincaré group
,” J. Math. Phys.
34
, 2045
–2058
(1993
).16.
M.
Klimek
, “Integrals of motion for some equations on q-Minkowski space
,” Czech. J. Phys.
47
, 1199
–1206
(1997
).17.
J. A.
Azcárraga
, P. P.
Kulish
, and F.
Rodenas
, “On the physical contents of q-deformed Minkowski spaces
,” Phys. Lett. B
351
, 123
–130
(1995
).18.
J. A.
Azcárraga
, P. P.
Kulish
, and F.
Rodenas
, “Quantum groups and deformed special relativity
,” Fortschr. Phys.
44
, 1
–40
(1996
).19.
S.
Majid
, “Braided geometry of the conformal algebra
,” J. Math. Phys.
37
, 6495
–6509
(1996
).20.
S.
Doplicher
, K.
Fredenhagen
, and J. E.
Roberts
, “The quantum structure of spacetime at the Planck scale and quantum fields
,” Commun. Math. Phys.
172
, 187
–220
(1995
).21.
S.
Doplicher
, K.
Fredenhagen
, and J. E.
Roberts
, “Spacetime quantization induced by classical gravity
,” Phys. Lett. B
331
, 39
–44
(1994
).22.
J.
Madore
and J.
Mourad
, “Quantum space–time and classical gravity
,” J. Math. Phys.
39
, 423
–442
(1998
).23.
Ch.
Chryssomalakos
, “Remarks on quantum integration
,” Commun. Math. Phys.
184
, 1
–25
(1997
).24.
Ch. Chryssomalakos, “Applications of quantum groups,” Ph.D. thesis, UC Berkeley, 1994.
25.
A.
Kempf
and S.
Majid
, “Algebraic q-integration and Fourier theory on quantum and braided spaces
,” J. Math. Phys.
35
, 6802
–6836
(1994
).
This content is only available via PDF.
© 1999 American Institute of Physics.
1999
American Institute of Physics
You do not currently have access to this content.
