Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle

Yacine Bouguerra; Mustapha Maamache; Jeong Ryeol Choi

doi:10.1088/1674-1137/41/6/065103

Chinese Physics C> 2017, Vol. 41> Issue(6) : 065103 DOI: 10.1088/1674-1137/41/6/065103

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle

1.
Laboratoire de Physique Quantique et Systé
2.
Dé
3.
Laboratoire de Physique Quantique et Systé
4.
Department of Radiologic Technology, Daegu Health College, Yeongsong-ro 15, Buk-gu, Daegu 41453, Republic of Korea

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Abstract：
Hannay's angle is a classical analogue of the “geometrical phase factor” found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay's angle is derived from a rigorous evaluation. The obtained Hannay's angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay's angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation, and its physical nature is addressed. Hannay's angle, together with its quantum counterpart Berry's phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation.
- Yang-Mills cosmology ,
- Hannay angle ,
- time-dependent quartic Hamiltnian ,
- inflation

References

[1]	D. V. Gal'tsov and E. A. Davydov, Int. J. Mod. Phys.: Conf. Ser., 14: 316 (2012)
[2]	D. V. Gal'tsov and E. A. Davydov, Proc. Steklov Inst. Math., 272: 119 (2011).
[3]	E. A. Davydov and D. V. Gal'tsov, Gravit. Cosmol., 21: 35 (2015)
[4]	D. V. Gal'tsov, Proceedings of the 43rd Rencontres de Moriond La Thuile J08, Gal'tsov(1-16) (2008). [arXiv:0901.0115v1 [gr-qc]]
[5]	V. V. Dyadichev, D. V. Gal'tsov, A. G. Zorin, and M. Yu. Zotov, Phys. Rev. D, 65: 084007 (2002)
[6]	Y. Q. Cai and G. Papini, Mod. Phys. Lett. A, 4: 1143 (1989)
[7]	F. Wilczek and A. Zee, Phys. Rev. Lett., 52: 2111 (1984)
[8]	Y. Q. Cai and G. Papini, Class. Quantum Grav., 7: 269 (1990)
[9]	S. Albeverio and S. Mazzucchi, J. Funct. Anal., 238: 471 (2006)
[10]	O. V. Usatenko, J.-P. Provost, G. Valle, and A. Boudine, Phys. Lett. A, 250: 99 (1998)
[11]	J. H. Hannay, J. Phys. A: Math. Gen., 18: 221 (1985)
[12]	D. H. Kobe and J. Zhu, Int. J. Mod. Phys. B, 7: 4827 (1993)
[13]	H. D. Liu, X. X. Yi, and L. B. Fu, Ann. Phys. (N.Y.), 339: 1 (2013)
[14]	A. K. Pati, Ann. Phys. (N.Y.), 270: 178 (1998)
[15]	O. V. Usatenko, J.-P. Provost, and G. Valle, J. Phys. A: Math. Gen., 29: 2607 (1996)
[16]	B. K. Pal, S. Pal, and B. Basu, Class. Quantum Grav., 30: 125002 (2013)
[17]	D. P. Datta, Phys. Rev. D, 48: 5746 (1993)
[18]	S. P. Kim, Phys. Lett. A, 191: 365 (1994)
[19]	D. P. Datta, Mod. Phys. Lett. A, 08: 601 (1993)
[20]	A. Mostafazadeh, Turk. J. Phys., 24: 411 (2000)
[21]	B. K. Pal, S. Pal, and B. Basu, J. Phys.: Conf. Ser., 405: 012025 (2012)
[22]	R. Brout and G. Venturi, Phys. Rev. D, 39: 2436 (1989)
[23]	H. Rosu, P. Espinoza, and M. Reyes, Il Nuovo Cimento B, 114: 1439 (1999)
[24]	A. D. A. M. Spallicci, Il Nuovo Cimento B, 119: 1215 (2004)
[25]	M. V. Berry and M. A. Morgan, Nonlinearity, 9: 787 (1996)
[26]	W. Zhao, Y. Zhang, and M. Tong, Quantum Yang-Mills condensate dark energy models, in Dark Energy: Theories, Developments and Implications, K. Lefebvre and R. Garcia(eds.), Ch. 5 (New York, Nova Science Publishers, Inc., 2010). pp. 89-110
[27]	Y. Zhang, T. Y. Xia, and W. Zhao, Class. Quantum Grav. 24: 3309 (2007)
[28]	T. Y. Xia and Y. Zhang, Phys. Lett. B, 656: 19 (2007)
[29]	S. Wang, Y. Zhang, and T. Y. Xia, J. Cosmol. Astropart. Phys., 2008: 037 (2008)
[30]	Y. Zhang, Phys. Lett. B, 340: 18 (1994)
[31]	P. A. R. Ade et al, Phys. Rev. Lett., 112: 241101 (2014)
[32]	P. A. R. Ade et al, arXiv: 1603.05976v1 (2016)
[33]	J. J. van der Bij and E. Radu, Int. J. Mod. Phys. A, 18: 2379 (2003)
[34]	G. D. Moore, Phys. Rev. D, 62: 085011 (2000)
[35]	S. Golin, J. Phys. A: Math. Gen., 22: 4573 (1989)
[36]	S. Golin, A. Knauf, and S. Marmi, Commun. Math. Phys., 123: 95 (1989)
[37]	S. Golin and S. Marmi, Europhys. Lett., 8: 399 (1989)
[38]	S. Golin and S. Marmi, Nonlinearity, 3: 507 (1990)
[39]	A. D. A. M. Spallicci, A. Morbidelli, and G. Metris, Nonlinearity, 18: 45 (2005)
[40]	C. A. Mead, Phys. Rev. Lett., 59: 161 (1987)
[41]	S. C. Li, J. Liu, and L. B. Fu, Phys. Rev. A, 83: 042107 (2011)
[42]	A. G. Wagh, V. C. Rakhecha, P. Fischer, and A. Ioffe, Phys. Rev. Lett., 81: 1992 (1998)

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[15]	Zhao Liu . Hamiltonian Reductions of Supersymmetric Self-Dual Yang-Mills Model. Chinese Physics C, 1993, 17(S4): 361-369.
[16]	Zhao Liu . Supersymmetrization of Self-Dual Yang-Mills Theory. Chinese Physics C, 1993, 17(S4): 347-353.
[17]	LI Fu-Bin . Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions. Chinese Physics C, 1992, 16(5): 408-413.
[18]	Li Fubin . A Study on the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equation System. Chinese Physics C, 1992, 16(S2): 155-161.
[19]	WU YONG-SHI . THE HOLONOMY FUNCTIONAL FORMULATION OF YANG-MILLS FIELD EQUATIONS. Chinese Physics C, 1979, 3(3): 382-386.
[20]	WU YONG-SHI , LEE HWA-CHUNG , KUO SHUO-HUNG , HSEEN TING-CHANG . ON A PSEUDO-PARTICLE SOLUTION OF THE YANG-MILLS FIELD. Chinese Physics C, 1978, 2(4): 371-373.

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Yacine Bouguerra, Mustapha Maamache and Jeong Ryeol Choi. Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle[J]. Chinese Physics C, 2017, 41(6): 065103. doi: 10.1088/1674-1137/41/6/065103

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Received: 2016-12-16
Revised: 2017-01-14

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Supported by Basic Science Research Program through National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)}

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沈阳化工大学材料科学与工程学院沈阳 110142

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle

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Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle

Corresponding author: Jeong Ryeol Choi,

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