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Seeley–DeWitt expansion of scattering phase shift

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Abstract

In this paper, we use the Seeley–DeWitt expansion of heat kernel method in quantum field theory to give an explicit expression of the perturbation expansion for the scattering phase shift for three-dimensional spherically symmetric potential scattering in quantum mechanics. The spectral function is defined by the eigenproblem of an operator, and the spectral functions are related by transforms. The heat kernel and the scattering phase shift are both spectral functions of the Hamiltonian. By a transform between the heat kernel and the scattering phase shift, we convert the Seeley–DeWitt expansion of heat kernels to an expansion of scattering phase shifts up to the first two orders.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We are very indebted to Dr G. Zeitrauman for his encouragement. This work is supported in part by Special Funds for theoretical physics Research Program of the NSFC under Grant No. 11947124, and NSFC under Grant Nos. 11575125 and 11675119.

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Authors and Affiliations

  1. Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin, 300071, People’s Republic of China

    Yuan-Yuan Liu & Yu-Jie Chen

  2. College of Physical Science and Technology, Bohai University, Jinzhou, 121013, People’s Republic of China

    Shi-Lin Li

  3. College of Physics and Materials Science, Tianjin Normal University, Tianjin, 300387, People’s Republic of China

    Wen-Du Li

  4. Department of Physics, Tianjin University, Tianjin, 300350, People’s Republic of China

    Yu-Jie Chen, Shi-Lin Li & Wu-Sheng Dai

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  1. Yuan-Yuan Liu
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Liu, YY., Chen, YJ., Li, SL. et al. Seeley–DeWitt expansion of scattering phase shift. Eur. Phys. J. Plus 137, 1140 (2022). https://doi.org/10.1140/epjp/s13360-022-03380-5

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