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Field-theoretical space-time position operator of the Dirac electron

Zhi-Yong Wang·Cai-Dong Xiong·Bing He
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Abstract

A field-theoretical space-time position operator can be properly introduced for the Dirac field, it plays the role of a generalized Noether charge associated with a local symmetry, and its second-quantized form shows that quantum fields possess zero-point time, which implies that a zero-point fluctuation of energy must be accompanied with a zero-point fluctuation of time, and then in agreement with the time-energy uncertainty principle. In practice, some possible physical effects owing to zero-point time remain to be found.

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Zhi-Yong Wang, Cai-Dong Xiong, Bing He. 2006-10-19. Field-theoretical space-time position operator of the Dirac electron. https://arxiv.org/abs/quant-ph/0610155

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