Tachyons and Representations of Sp(2, R)
139
such tachyonic representations for describing constituents in the construction of
elementary particles like the muon [13]. In fact, since tachyons cannot exist as
physically observable particles, it provides a method of confinement similar to
the kinematical confinement of Flato and Fronsdal in their description of massless
particles as tensor products of Di’s and Rac’s [14].
References
1. P. Moylan, Parallelizations for induced representations of SO(2,q), in Proceedings in Mathematics and Statistics, ed. by V.K. Dobrev, vol. 263 (Springer, Berlin, 2018). https://doi.org/10.
1007/978-981-13-2715-5_12
2. A.W. Knapp, Representation Theory of Semisimple Groups: An Overview Based on Examples
(Princeton University Press, Princeton, 2001)
3. P. Bozek, M. Havlíˇ cek, O. Navrátil, Charles Univ. Preprint (1985)
4. M. Havlíˇ cek, P. Moylan, J. Math. Phys. 34(11), 5320–5332 (1993)
5. P. Moylan, Representations of classical Lie algebras from their quantum deformations, in
Institute of Physics Conference Series, ed. by J.P. Gazeau, R. Kerner, vol. 173 (CRC Press,
Boca Raton, FL, 2003), pp. 683–687
6. P. Moylan, Tachyons and representations of the de Sitter groups (Chapter 2), in Studies in
Mathematical Physics Research, ed. by C.V. Benton (Nova Science, Piscataway, NJ, 2004)
7. V.K. Dobrev, P. Moylan, Elementary intertwining operators for SU(2,2): II. Fortschr. der Phys.
42, 339–392 (1994)
8. J. Hebda, P. Moylan, A topological criterion for group decompositions. Math. Proc. Camb.
Phil. Soc. 103, 285–298 (1988)
9. A.H. Dooley, J.W. Rice, On contractions of semisimple Lie groups. Trans. Am. Math. Soc.
289, 185–202 (1985)
10. J.B. Ehrman, On the unitary irreducible representations of the universal covering group of the
3+2 DeSitter group. Math. Proc. Cambr. Phil. Soc. 53, 290 (1956)
11. N.T. Evans, Discrete series for the universal covering group of the 3 + 2 de Sitter group. J.
Math. Phys. 8, 170 (1967)
12. P.C.W. Davies, Tachyonic dark matter, arXiv:astro-ph/0403048 (2004). https://arxiv.org/abs/
astro-ph/0403048
13. P. Moylan, Mass formulae for the Pion and Muon, Preprint: 88-0038 Sofia, BG (1988). http://
inspirehep.net/record/22955/
14. M. Flato, C. Fronsdal, Interacting singletons. Lett. Math. Phys. 44, 249–259 (1998)
15. E.P. Wigner, On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40,
149–204 (1939)
16. V. Bargmann, E.P. Wigner, Group theoretical discussion of relativistic wave equations. Proc.
Nat. Acad. Sci. (USA) 34(5), 211–223 (1948). https://doi.org/10.1073/pnas.34.5.211
139
such tachyonic representations for describing constituents in the construction of
elementary particles like the muon [13]. In fact, since tachyons cannot exist as
physically observable particles, it provides a method of confinement similar to
the kinematical confinement of Flato and Fronsdal in their description of massless
particles as tensor products of Di’s and Rac’s [14].
References
1. P. Moylan, Parallelizations for induced representations of SO(2,q), in Proceedings in Mathematics and Statistics, ed. by V.K. Dobrev, vol. 263 (Springer, Berlin, 2018). https://doi.org/10.
1007/978-981-13-2715-5_12
2. A.W. Knapp, Representation Theory of Semisimple Groups: An Overview Based on Examples
(Princeton University Press, Princeton, 2001)
3. P. Bozek, M. Havlíˇ cek, O. Navrátil, Charles Univ. Preprint (1985)
4. M. Havlíˇ cek, P. Moylan, J. Math. Phys. 34(11), 5320–5332 (1993)
5. P. Moylan, Representations of classical Lie algebras from their quantum deformations, in
Institute of Physics Conference Series, ed. by J.P. Gazeau, R. Kerner, vol. 173 (CRC Press,
Boca Raton, FL, 2003), pp. 683–687
6. P. Moylan, Tachyons and representations of the de Sitter groups (Chapter 2), in Studies in
Mathematical Physics Research, ed. by C.V. Benton (Nova Science, Piscataway, NJ, 2004)
7. V.K. Dobrev, P. Moylan, Elementary intertwining operators for SU(2,2): II. Fortschr. der Phys.
42, 339–392 (1994)
8. J. Hebda, P. Moylan, A topological criterion for group decompositions. Math. Proc. Camb.
Phil. Soc. 103, 285–298 (1988)
9. A.H. Dooley, J.W. Rice, On contractions of semisimple Lie groups. Trans. Am. Math. Soc.
289, 185–202 (1985)
10. J.B. Ehrman, On the unitary irreducible representations of the universal covering group of the
3+2 DeSitter group. Math. Proc. Cambr. Phil. Soc. 53, 290 (1956)
11. N.T. Evans, Discrete series for the universal covering group of the 3 + 2 de Sitter group. J.
Math. Phys. 8, 170 (1967)
12. P.C.W. Davies, Tachyonic dark matter, arXiv:astro-ph/0403048 (2004). https://arxiv.org/abs/
astro-ph/0403048
13. P. Moylan, Mass formulae for the Pion and Muon, Preprint: 88-0038 Sofia, BG (1988). http://
inspirehep.net/record/22955/
14. M. Flato, C. Fronsdal, Interacting singletons. Lett. Math. Phys. 44, 249–259 (1998)
15. E.P. Wigner, On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40,
149–204 (1939)
16. V. Bargmann, E.P. Wigner, Group theoretical discussion of relativistic wave equations. Proc.
Nat. Acad. Sci. (USA) 34(5), 211–223 (1948). https://doi.org/10.1073/pnas.34.5.211