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

  • 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.
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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
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 shu
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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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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
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.

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