Research PaperNo Access

Thermal Lie superalgebras

Marco A. S. Trindade

https://orcid.org/0000-0001-5584-222X

Colegiado de Física, Departamento de Ciências Exatas e da Terra, Universidade do Estado da Bahia, Bahia, Brazil

E-mail Address: matrindade@uneb.br

Corresponding author.

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and

Eric Pinto

Instituto de Física, Universidade Federal da Bahia, Bahia, Brazil

E-mail Address: ericpinto@protonmail.com

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https://doi.org/10.1142/S0217751X21502377Cited by:0 (Source: Crossref)

Abstract

In this paper, we derive a general formulation for thermal Lie superalgebras motivated by thermofield dynamics formalism (TFD). Particularly, we construct the thermal Poincaré superalgebras. The operators in TFD are defined through the doubling of the degrees of freedom of the system and it can be related to Hopf algebras. In this way, we explore the notion of quantum group associated with these superalgebras and we show the noncommutativity in this thermal scenario. Furthermore, the thermal M-superalgebra is also derived from TFD prescription.

Keywords:

PACS: 03.65.Ca, 03.65.Fd

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References

1. J. Wess and J. Bagger , Supersymmetry and Supergravity (Princeton University Press, Princeton, 1983). Crossref, Google Scholar
2. P. J. O. Freund , Introduction to Supersymmetry, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 1986). Crossref, Google Scholar
3. M. F. Sohnius , Phys. Rep. 128, 39 (1985). Crossref, Web of Science, ADS, Google Scholar
4. V. Salnikov , Russ. J. Math. Phys. 27, 517 (2020). Crossref, Web of Science, Google Scholar
5. V. Kac , Adv. Math. 26, 8 (1977). Crossref, Web of Science, Google Scholar
6. M. R. Traubenberg , Adv. Appl. Clifford Algebr. 19, 868 (2009). Crossref, Web of Science, Google Scholar
7. M. Kaku , Introduction to Superstring and M-Theory, 2nd edn. (Springer-Verlag, New York, 1999). Crossref, Google Scholar
8. F. Toppan and J. Lukierski , Int. J. Mod. Phys. A 18, 2135 (2003). Link, Web of Science, ADS, Google Scholar
9. F. Toppan and J. Lukierski , Phys. Lett. B 567, 125 (2003). Crossref, Web of Science, ADS, Google Scholar
10. P. Townsend, p-brane democracy, arXiv:hep-th/9507048. Google Scholar
11. J. V. Holten and A. V. Proyen , J. Phys. A 15, 3763 (1982). Crossref, ADS, Google Scholar
12. D. Nedel, M. C. Abdalla and A. L. Gadelha , Phys. Lett. B 598, 121 (2004). Crossref, Web of Science, ADS, Google Scholar
13. Y. Takahashi and H. Umezawa , Coll. Phenom. 2, 55 (1975). Web of Science, Google Scholar
14. Y. Takahashi and H. Umezawa , Int. J. Mod. Phys. B 10, 1755 (1996). Link, Web of Science, ADS, Google Scholar
15. F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malbouisson and A. E. Santana , Thermal Quantum Field Theory: Algebraic Aspects and Applications (World Scientific, Singapore, 2009). Link, Google Scholar
16. H. Matsumoto, N. Nakahara, Y. Nakano and H. Umezawa , Phys. Rev. D 29, 2838 (1984). Crossref, Web of Science, ADS, Google Scholar
17. A. E. Santana, A. Matos Neto, J. D. M. Vianna and F. C. Khanna , Int. J. Theor. Phys. 38, 641 (1999). Crossref, Web of Science, Google Scholar
18. M. Takesaki and M. Tomita , Theory of Modular Hilbert Algebras and its Applications (Springer-Verlag, Berlin, 1970). Crossref, Google Scholar
19. I. Ojima , Ann. Phys. 137, 1 (1981). Crossref, Web of Science, ADS, Google Scholar
20. O. Bratelli and D. W. Robinson , Operators Algebras and Quantum Statistical Mechanics, Vols. I and II (Springer-Verlag, Berlin, 1997). Crossref, Google Scholar
21. A. E. Santana and F. C. Khanna , Phys. Lett. A 203, 68 (1995). Crossref, Web of Science, ADS, Google Scholar
22. T. Kopf, A. E. Santana and F. C. Khanna , J. Math. Phys. 38, 4971 (1997). Crossref, Web of Science, ADS, Google Scholar
23. E. Celeghini, S. De Martino, S. De Siena, A. Iorio, M. Rasetti and G. Vitiello , Phys. Lett. A 244, 455 (1998). Crossref, Web of Science, ADS, Google Scholar
24. S. Majid , Foundations of Quantum Group Theory (Cambridge University Press, Cambridge, 1995). Crossref, Google Scholar
25. V. Chari and A. Pressley , A Guide to Quantum Groups (Cambridge University Press, Cambridge, 1994). Google Scholar
26. I. M. Burban , J. Nonlin. Math. Phys. 2, 114 (1995). Crossref, Google Scholar
27. N. Reshetikhin , Lett. Math. Phys. 20, 331 (1990). Crossref, Web of Science, ADS, Google Scholar
28. Y. Kobayashi and S. Sasaki , Int. J. Mod. Phys. A 20, 7175 (2005). Link, Web of Science, ADS, Google Scholar
29. V. P. Nair , Phys. Rev. D 92, 104009-1 (2015). Crossref, Web of Science, ADS, Google Scholar
30. W. Taylor IV , Rev. Mod. Phys. 73, 419 (2001). Crossref, Web of Science, ADS, Google Scholar
31. H. J. W. Müller and A. Weidmann , Supersymmetry: An Introduction with Conceptual and Calculational Details (World Scientific, Singapore, 1987). Google Scholar
32. A. Anastasiou, L. Borsten, M. J. Duff, L. J. Hughes and S. Nagy , J. High Energy Phys. 22, 1 (2014). Google Scholar
33. Y. Su, X. Yue and X. Zhu , J. Geom. Phys. 160, 103987 (2021). Crossref, Web of Science, Google Scholar