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

Abstract
HTML
Reference
Related

PDF

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)

[1]	Renli Xu , Chen Wu , Jian Liu , Bin Hong , Jie Peng , Xiong Li , Ruxian Zhu , Zhizhen Zhao , Zhongzhou Ren . Ground-state properties of finite nuclei in relativistic Hartree-Bogoliubov theory with an improved quark mass density-dependent model. Chinese Physics C, 2026, 50(2): 1-12.
[2]	. Testing Einstein-Maxwell Power-Yang-Mills hair via black hole photon rings. Chinese Physics C, 2026, 50(1): 015101. doi: 10.1088/1674-1137/ae039c
[3]	Siyu Tang , Zuman Zhang , Chao Zhang , Liang Zheng , Renzhuo Wan . Investigating the transverse-momentum- and pseudorapidity-dependent flow vector decorrelation in p–Pb collisions with a multi-phase transport model. Chinese Physics C, 2025, 49(12): 124104. doi: 10.1088/1674-1137/adef1b
[4]	Tetsuaki Moriguchi , Momo Mukai , Naoto Kaname , Akira Ozawa , Shinji Suzuki , Yasushi Abe , Hiroki Arakawa , Tomoya Fujii , Daiki Hamakawa , Sakumi Harayama , Shun Hosoi , Yasuto Inada , Kumi Inomata , Reo Kagesawa , Daisuke Kajiki , Daiki Kamioka , Masanori Kanda , Atsushi Kitagawa , Takaaki Kobayashi , Daisuke Nagae , Sarah Naimi , Kunimitsu Nishimuro , Shunichiro Omika , Misaki Otsu , Mamoru Sakaue , Shinji Sato , Hibiki Seki , Naru Shinozaki , Takeshi Suzuki , Keisuke Tomita , Takayuki Yamaguchi , Yoshitaka Yamaguchi , Asahi Yano , Kenjiro Yokota . Improvements of time-of-flight detector utilizing a thin foil and crossed static electric and magnetic fields. Chinese Physics C, 2025, 49(10): 104001. doi: 10.1088/1674-1137/ade95b
[5]	Erdem Sucu , İzzet Sakallı . Quantum tunneling and Aschenbach effect in nonlinear Einstein-Power-Yang-Mills AdS black holes. Chinese Physics C, 2025, 49(10): 105101. doi: 10.1088/1674-1137/add8fe

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Fund

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

Article Metric

Article Views(2689)
PDF Downloads(41)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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

Corresponding author: Jeong Ryeol Choi,

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

Received Date: 2016-12-16

Accepted Date: 2017-01-14

Available Online: 2017-06-05

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

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.

HTML

Reference (42)

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

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article