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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.12771 |
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| _version_ | 1866908637060923392 |
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| author | Witten, Edward |
| author_facet | Witten, Edward |
| contents | Quantum mechanics requires a hermitian inner product <~,~> -- linear in one variable, antilinear in the other -- while the inner product (~,~) that comes most naturally from Euclidean path integrals is linear in each variable. Here we discuss the relation between the two inner products. In a theory with no time-reversal or reflection symmetry, they differ by an operator that complex conjugates the wavefunction and reverses the orientation of space; in the presence of reflection and time-reversal symmetry, space is unoriented so such an operator cannot be defined, but the time-reversal symmetry T is available instead and plays the same role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bras and Kets in Euclidean Path Integrals Witten, Edward High Energy Physics - Theory Quantum mechanics requires a hermitian inner product <~,~> -- linear in one variable, antilinear in the other -- while the inner product (~,~) that comes most naturally from Euclidean path integrals is linear in each variable. Here we discuss the relation between the two inner products. In a theory with no time-reversal or reflection symmetry, they differ by an operator that complex conjugates the wavefunction and reverses the orientation of space; in the presence of reflection and time-reversal symmetry, space is unoriented so such an operator cannot be defined, but the time-reversal symmetry T is available instead and plays the same role. |
| title | Bras and Kets in Euclidean Path Integrals |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.12771 |