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  • Open Access

QFT in Klein space

Bin Chen1,2,3,4,*, Zezhou Hu2,†, and Xin-Cheng Mao2,‡

  • 1Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, People’s Republic of China
  • 2School of Physics, Peking University, No. 5 Yiheyuan Road, Beijing 100871, People’s Republic of China
  • 3Center for High Energy Physics, Peking University, No. 5 Yiheyuan Road, Beijing 100871, People’s Republic of China
  • 4Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, People’s Republic of China

  • *Contact author: chenbin1@nbu.edu.cn
  • †Contact author: z.z.hu@pku.edu.cn
  • ‡Contact author: maoxc1120@stu.pku.edu.cn
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Phys. Rev. D 113, 085005 – Published 3 April, 2026

DOI: https://doi.org/10.1103/y1sk-kh72

Abstract

In this paper, we investigate the quantum field theory in Klein space that has two time directions. To study the canonical quantization, we select the “length of time” q as the evolution direction of the system. In our novel construction, some additional modes beyond the plane wave modes are crucial in the canonical quantization and the later derivation of the Lehmann-Symanzik-Zimmermann reduction formula. We also derive the free two-point function by using Wick contraction in the canonical quantization formalism. Moreover, we introduce the path-integral formalism in which we can redefine the vacuum states and rederive the correlation functions. We show that all the results in the Klein space derived in our novel approach match those obtained via analytical continuation from the Minkowski spacetime.

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See Also

Quantum field theory in flat spacetime with multiple time directions

Bin Chen, Zezhou Hu, and Xin-Cheng Mao
Phys. Rev. D 112, 085008 (2025)

Article Text

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Phys. Rev. D 113, 085005– Published 3 April, 2026
  • Received 27 November 2025
  • Accepted 13 March 2026
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