- Letter
- Open Access
Interference and oscillation in Nambu quantum mechanics
Phys. Rev. D 104, L051301 – Published 10 September, 2021
DOI: https://doi.org/10.1103/PhysRevD.104.L051301
Abstract
Nambu quantum mechanics, proposed in [Phys. Lett. B 536, 305 (2002)], is a deformation of canonical quantum mechanics in which only the time-evolution of the “phases” of energy eigenstates is modified. We discuss the effect this theory will have on oscillation phenomena, and place a bound on the deformation parameters utilizing the data on the atmospheric neutrino mixing angle .
Physics Subject Headings (PhySH)
Article Text
References (68)
- I. H. Deutsch, PRX Quantum 1, 020101 (2020).
- J. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England, 2004).
- Y. Aharonov and D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley-VCH, New York, 2005).
- G. ’t Hooft, arXiv:1405.1548.
- R. Penrose, Found. Phys. 44, 557 (2014).
- M. Gell-Mann and J. B. Hartle, Phys. Rev. A 89, 052125 (2014).
- S. Weinberg, Phys. Rev. A 93, 032124 (2016).
- A. Leggett, Prog. Theor. Phys. Suppl. 170, 100 (2007).
- E. C. G. Stueckelberg, Helv. Phys. Acta 33, 727 (1960), https://www.e-periodica.ch/cntmng?pid=hpa-001%3A1960%3A33%3A%3A1097.
- S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, Oxford, UK, 1995).
- M. Gunaydin, C. Piron, and H. Ruegg, Commun. Math. Phys. 61, 69 (1978).
- S. Okubo, Introduction to Octonion and Other Non-Associative Algebras in Physics, Montroll Memorial Lecture Series in Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
- F. Gursey and C. H. Tze, On the Role of Division, Jordan and Related Algebras in Particle Physics (World Scientific, Singapore, 1996).
- L. N. Chang, Z. Lewis, D. Minic, and T. Takeuchi, Mod. Phys. Lett. B 27, 1350064 (2013).
- L. N. Chang, Z. Lewis, D. Minic, and T. Takeuchi, J. Phys. A 46, 065304 (2013).
- L. N. Chang, Z. Lewis, D. Minic, and T. Takeuchi, J. Phys. A 46, 485306 (2013).
- T. Takeuchi, L. N. Chang, Z. Lewis, and D. Minic, AIP Conf. Proc. 1508, 502 (2012).
- L. N. Chang, Z. Lewis, D. Minic, and T. Takeuchi, Int. J. Mod. Phys. A 29, 1430006 (2014).
- L. N. Chang, Z. Lewis, D. Minic, and T. Takeuchi, J. Phys. A 47, 405304 (2014).
- L. N. Chang, D. Minic, and T. Takeuchi, J. Phys. Conf. Ser. 1275, 012036 (2019).
- S. Weinberg, Phys. Rev. Lett. 62, 485 (1989).
- S. Weinberg, Ann. Phys. (N.Y.) 194, 336 (1989).
- D. Minic and C. H. Tze, Phys. Lett. B 536, 305 (2002).
- Y. Nambu, Phys. Rev. D 7, 2405 (1973).
- T. Kibble, Commun. Math. Phys. 65, 189 (1979).
Mathematica encodes , , and respectively as JacobiSN[,], JacobiCN[, ], and JacobiDN[, ] with .
Mathematica encodes as EllipticK[] with .
- T. Opatrný, L. Richterek, and M. Opatrný, Sci. Rep. 8, 1984 (2018).
- I. D. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged ed., edited by A. Jeffery (Academic Press, New York, 2014).
- M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Martino publishing, Mansfield Centre, CT, 2014).
- E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 3rd ed. (Dover Publications, New York, 2020).
- U. Nierste, in Proceedings of the Helmholz International School “Heavy Quark Physics” (HPQ08), edited by A. Ali and M. Ivanov (DESY, Hamburg, Germany, 2009), pp. 1–37 [].
- B. Kayser, AIP Conf. Proc. 1441, 464 (2012).
- P. de Salas, D. Forero, S. Gariazzo, P. Martínez-Miravé, O. Mena, C. Ternes, M. Tórtola, and J. Valle, J. High Energy Phys. 02 (2021) 071.
- A. Terliuk (IceCube Collaboration), Proc. Sci., NOW2018 (2019) 007.
- W.-l. Guo (JUNO Collaboration), J. Phys. Conf. Ser. 888, 012205 (2017).
- A. Higuera (DUNE Collaboration), Proc. Sci., EPS-HEP2017 (2018) 115.
- A. Peres, Phys. Rev. Lett. 42, 683 (1979).
- S. Gstir, E. Chan, T. Eichelkraut, A. Szameit, R. Keil, and G. Weihs, arXiv:2104.11577.
- L. Takhtajan, Commun. Math. Phys. 160, 295 (1994).
- G. Dito, M. Flato, D. Sternheimer, and L. Takhtajan, Commun. Math. Phys. 183, 1 (1997).
- G. Dito and M. Flato, Lett. Math. Phys. 39, 107 (1997).
- E. Bergshoeff, E. Sezgin, Y. Tanii, and P. Townsend, Ann. Phys. (N.Y.) 199, 340 (1990).
- H. Awata and D. Minic, J. High Energy Phys. 04 (1998) 006.
- H. Awata, M. Li, D. Minic, and T. Yoneya, J. High Energy Phys. 02 (2001) 013.
- K. Fujikawa and K. Okuyama, Phys. Lett. B 411, 261 (1997).
- L. Smolin, Phys. Rev. D 57, 6216 (1998).
- T. L. Curtright and C. K. Zachos, Phys. Rev. D 68, 085001 (2003).
- T. L. Curtright and C. K. Zachos, New J. Phys. 4, 83 (2002).
- T. L. Curtright and C. K. Zachos, AIP Conf. Proc. 672, 165 (2003).
- J. A. Bagger and N. Lambert, Phys. Rev. D 77, 065008 (2008).
- A. Gustavsson, Nucl. Phys. B811, 66 (2009).
- C.-S. Chu, P.-M. Ho, Y. Matsuo, and S. Shiba, J. High Energy Phys. 08 (2008) 076.
- P.-M. Ho and Y. Matsuo, Prog. Theor. Exp. Phys. 2016, 06A104 (2016).
- L. Freidel, R. G. Leigh, and D. Minic, Int. J. Mod. Phys. A 34, 1941004 (2019).
- D. Minic, in 10th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics (2020), pp. 183–218 [arXiv:2003.00318].
- P. Berglund, T. Hübsch, and D. Minić, Phys. Lett. B 798, 134950 (2019).
- P. Berglund, T. Hübsch, and D. Minic, Lett. High Energy Phys. 2021, 186 (2021).
- L. Freidel, R. G. Leigh, and D. Minic, Phys. Lett. B 730, 302 (2014).
- L. Freidel, R. G. Leigh, and D. Minic, Int. J. Mod. Phys. D 23, 1442006 (2014).
- L. Freidel, R. G. Leigh, and D. Minic, J. High Energy Phys. 06 (2015) 006.
- L. Freidel, R. G. Leigh, and D. Minic, Phys. Rev. D 94, 104052 (2016).
- L. Freidel, R. G. Leigh, and D. Minic, J. Phys. Conf. Ser. 804, 012032 (2017).
- L. Freidel, R. G. Leigh, and D. Minic, J. High Energy Phys. 09 (2017) 060.
- L. Freidel, R. G. Leigh, and D. Minic, Phys. Rev. D 96, 066003 (2017).
- L. Freidel, J. Kowalski-Glikman, R. G. Leigh, and D. Minic, Phys. Rev. D 99, 066011 (2019).
- G. G. Raffelt, Phys. Rev. D 83, 105022 (2011).
- Y. Pehlivan, A. B. Balantekin, T. Kajino, and T. Yoshida, Phys. Rev. D 84, 065008 (2011).