Spectral decomposition of field operators and causal measurement in quantum field theory
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916672332365824 |
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| author | Oeckl, Robert |
| author_facet | Oeckl, Robert |
| contents | We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of positive-operator-valued measure decompositions. The latter arise from integrals over families of bounded positive operators. Crucially, these operators have the same locality properties as the underlying field operators. We use the decompositions to construct families of quantum operations implementing measurements of the field observables. Again, the quantum operations have the same locality properties as the field operators. What is more, we show that these quantum operations do not lead to superluminal signaling and are possible measurements on quantum fields in the sense of Sorkin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral decomposition of field operators and causal measurement in quantum field theory Oeckl, Robert High Energy Physics - Theory Mathematical Physics Functional Analysis Spectral Theory Quantum Physics We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of positive-operator-valued measure decompositions. The latter arise from integrals over families of bounded positive operators. Crucially, these operators have the same locality properties as the underlying field operators. We use the decompositions to construct families of quantum operations implementing measurements of the field observables. Again, the quantum operations have the same locality properties as the field operators. What is more, we show that these quantum operations do not lead to superluminal signaling and are possible measurements on quantum fields in the sense of Sorkin. |
| title | Spectral decomposition of field operators and causal measurement in quantum field theory |
| topic | High Energy Physics - Theory Mathematical Physics Functional Analysis Spectral Theory Quantum Physics |
| url | https://arxiv.org/abs/2409.08748 |