Mixed states for reference frames transformations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918400664535040 |
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| author | Fiore, Gaetano Lizzi, Fedele |
| author_facet | Fiore, Gaetano Lizzi, Fedele |
| contents | We discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the parameters' space, and they form a group. It is however possible that the distributions in the parameters' space are mixed states; such states form a semigroup. Similarly, transformations among quantum reference frames can be either pure or mixed. This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. This can also be discussed in relation to the time/energy uncertainty relation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_05758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed states for reference frames transformations Fiore, Gaetano Lizzi, Fedele Quantum Physics High Energy Physics - Theory Mathematical Physics Group Theory We discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the parameters' space, and they form a group. It is however possible that the distributions in the parameters' space are mixed states; such states form a semigroup. Similarly, transformations among quantum reference frames can be either pure or mixed. This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. This can also be discussed in relation to the time/energy uncertainty relation. |
| title | Mixed states for reference frames transformations |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics Group Theory |
| url | https://arxiv.org/abs/2507.05758 |