Basic Theory of Fractional Conformal Invariance of Mei Symmetry and its Applications to Physics |
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Authors: | Shao-Kai Luo Yun Dai Ming-Jing Yang Xiao-Tian Zhang |
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Institution: | 1.Institute of Theoretical Physics,Zhejiang Sci-Tech University,Hangzhou,China;2.Institute of Mathematical Mechanics and Mathematical Physics,Zhejiang Sci-Tech University,Hangzhou,People’s Republic of China |
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Abstract: | In this paper, we present a basic theory of fractional dynamics, i.e., the fractional conformal invariance of Mei symmetry, and find a new kind of conserved quantity led by fractional conformal invariance. For a dynamical system that can be transformed into fractional generalized Hamiltonian representation, we introduce a more general kind of single-parameter fractional infinitesimal transformation of Lie group, the definition and determining equation of fractional conformal invariance are given. And then, we reveal the fractional conformal invariance of Mei symmetry, and the necessary and sufficient condition whether the fractional conformal invariance would be the fractional Mei symmetry is found. In particular, we present the basic theory of fractional conformal invariance of Mei symmetry and it is found that, using the new approach, we can find a new kind of conserved quantity; as a special case, we find that an autonomous fractional generalized Hamiltonian system possesses more conserved quantities. Also, as the new method’s applications, we, respectively, find the conserved quantities of a fractional general relativistic Buchduhl model and a fractional Duffing oscillator led by fractional conformal invariance of Mei symmetry. |
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