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Ward-Takahashi identity in the light-front formalism for a bound state of fermions

Deepesh Bhamre* and J. P. B. C. de Melo†

  • *Contact author: deepeshbhamre7@gmail.com
  • †Contact author: joao.mello@cruzeirodosul.edu.br
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Phys. Rev. D 113, 036015 – Published 17 February, 2026

DOI: https://doi.org/10.1103/jm5x-7d83

Abstract

We investigate the Ward-Takahashi identity at one-loop in the light-front (LF) formalism for a bound state of fermions. We consider a spinless bound state made up of two fermions in which the Ward-Takahashi identity is satisfied in the covariant formulation. Considering the same system in the light-front formalism, we investigate the proof of Ward-Takahashi identity by integrating the light-front energy component through the identification of the relevant ranges of the longitudinal LF momentum. We elucidate that the pair production diagram plays a crucial role in establishing the Ward-Takahashi identity. We also point out the necessity of taking into account the corresponding zero modes for truly establishing the Ward-Takahashi identity in the LF formalism.

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Phys. Rev. D 113, 036015– Published 17 February, 2026
  • Received 14 November 2025
  • Accepted 14 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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