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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.17361 |
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| _version_ | 1866909975647879168 |
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| author | Zhou, Chi-Chun Chen, Shuai A. Chen, Yu-Zhu Shen, Yao Zhang, Fu-Lin Dai, Wu-Sheng |
| author_facet | Zhou, Chi-Chun Chen, Shuai A. Chen, Yu-Zhu Shen, Yao Zhang, Fu-Lin Dai, Wu-Sheng |
| contents | Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional principle has for 80 years remained a fundamental conceptual gap. Here we close this gap by establishing a no-go theorem that excludes any particle exchange statistics beyond bosons and fermions in three dimensions. We identify the consistency conditions linking the many-body Hilbert-space structure of quantum mechanics with the statistical microstate counting of indistinguishable particles. As a corollary, we demonstrate that higher-dimensional representations of the symmetric group cannot give rise to genuinely distinct particle exchange statistics in any spatial dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Statistics Forbids Particle Exchange Statistics beyond Bosons and Fermions in 3D Zhou, Chi-Chun Chen, Shuai A. Chen, Yu-Zhu Shen, Yao Zhang, Fu-Lin Dai, Wu-Sheng Quantum Physics Mathematical Physics Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional principle has for 80 years remained a fundamental conceptual gap. Here we close this gap by establishing a no-go theorem that excludes any particle exchange statistics beyond bosons and fermions in three dimensions. We identify the consistency conditions linking the many-body Hilbert-space structure of quantum mechanics with the statistical microstate counting of indistinguishable particles. As a corollary, we demonstrate that higher-dimensional representations of the symmetric group cannot give rise to genuinely distinct particle exchange statistics in any spatial dimension. |
| title | Quantum Statistics Forbids Particle Exchange Statistics beyond Bosons and Fermions in 3D |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2505.17361 |