Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Determination of infinitesimal generators on de Sitter space-time

Document Type : Original Article

Author
Department of Physics, Razi University, Kermanshah, Iran
Abstract
In this work, we study the motion of a free particle on 1+3-de Sitter space-time and introduce the associated symmetric group. We also present ten one-parameter subgroups of this group and derive the corresponding algebraic bases (or the Lie algebra of de Sitter group). Finally, by these subgroups, we introduce ten associated infinitesimal generators on 1+3-de Sitter space-time.
Keywords
Subjects

1. S. Weinberg, Gravitation and Cosmology: Principles 
and Applications of 260 the General Theory of Relativ
ity (Wiley, New York, 1972) #

2. L. Amendola, S. Tsujikawa, Dark energy theory and ob
servations (Cambridge University Press, New York, 
2010) #

3.   P. J. E. Peebles, B. Ratra, Rev. Modern Phy. 75, 2, 
(2003). J. M. Smith, Molecular Dynamics (Springer, 
Berlin, Heidelberg, 1987) #

4. N. Aghanim,  Planck Collaboration, Planck 2018 results. 
VI. Cosmological parameters, 2018, arXiv:1807.06209. 
5. A.Rabeie, Eur. Phys. J. C, 72  (2012) #

6. A.W. Knapp, Representation Theory of Semi-simple 
Groups (Princeton, NJ: Princeton University Press, 
1986) #

7. R. Takahashi, Bull. Soc. Math. 91 (1963). #

8. H. Bacry, J. M. Levey-Leblond, J. Math. Phys. 9  (1968)#
 
Volume 1, Issue 3
Summer 2024
Pages 72-76

  • Receive Date 16 July 2024
  • Revise Date 24 July 2024
  • Accept Date 11 August 2024
  • First Publish Date 11 August 2024
  • Publish Date 01 August 2024