Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian. Using C, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
This research output has an Altmetric Attention Score of 9. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 05 October 2021.
All research outputs
#4,782,319
of 29,155,047 outputs
Outputs from Physical Review Letters
#11,695
of 44,284 outputs
Outputs of similar age
#15,390
of 153,930 outputs
Outputs of similar age from Physical Review Letters
#5
of 107 outputs
Altmetric has tracked 29,155,047 research outputs across all sources so far. Compared to these this one has done well and is in the 83rd percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 44,284 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 13.9. This one has gotten more attention than average, scoring higher than 73% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 153,930 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 89% of its contemporaries.
We're also able to compare this research output to 107 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 95% of its contemporaries.
