Comparing Hermitian and Non-Hermitian Quantum Electrodynamics
In recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1816 |
| _version_ | 1797482044610052096 |
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| author | Jake Southall Daniel Hodgson Robert Purdy Almut Beige |
| author_facet | Jake Southall Daniel Hodgson Robert Purdy Almut Beige |
| author_sort | Jake Southall |
| collection | DOAJ |
| description | In recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for local electric and magnetic field observables and leads to a natural local biorthogonal description of the quantised electromagnetic field. When comparing this description with an alternative local Hermitian description, in which the states of local photonic particles, i.e., of so-called bosons localised in position (blips), are orthogonal under the conventional Hermitian inner product, we find that there is an equivalence between the two approaches. Careful consideration needs to be given to the physical interpretation of the different descriptions. Whether a Hermitian or a non-Hermitian approach is more suitable depends on the circumstances that we want to model. |
| first_indexed | 2024-03-09T22:22:42Z |
| format | Article |
| id | doaj.art-f881a55961de4fdf824cad3a4f71125e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:22:42Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f881a55961de4fdf824cad3a4f71125e2023-11-23T19:11:25ZengMDPI AGSymmetry2073-89942022-09-01149181610.3390/sym14091816Comparing Hermitian and Non-Hermitian Quantum ElectrodynamicsJake Southall0Daniel Hodgson1Robert Purdy2Almut Beige3The School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UKThe School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UKThe School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UKThe School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UKIn recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for local electric and magnetic field observables and leads to a natural local biorthogonal description of the quantised electromagnetic field. When comparing this description with an alternative local Hermitian description, in which the states of local photonic particles, i.e., of so-called bosons localised in position (blips), are orthogonal under the conventional Hermitian inner product, we find that there is an equivalence between the two approaches. Careful consideration needs to be given to the physical interpretation of the different descriptions. Whether a Hermitian or a non-Hermitian approach is more suitable depends on the circumstances that we want to model.https://www.mdpi.com/2073-8994/14/9/1816quantum electrodynamicsquantum opticsnon-Hermitian quantum physics |
| spellingShingle | Jake Southall Daniel Hodgson Robert Purdy Almut Beige Comparing Hermitian and Non-Hermitian Quantum Electrodynamics Symmetry quantum electrodynamics quantum optics non-Hermitian quantum physics |
| title | Comparing Hermitian and Non-Hermitian Quantum Electrodynamics |
| title_full | Comparing Hermitian and Non-Hermitian Quantum Electrodynamics |
| title_fullStr | Comparing Hermitian and Non-Hermitian Quantum Electrodynamics |
| title_full_unstemmed | Comparing Hermitian and Non-Hermitian Quantum Electrodynamics |
| title_short | Comparing Hermitian and Non-Hermitian Quantum Electrodynamics |
| title_sort | comparing hermitian and non hermitian quantum electrodynamics |
| topic | quantum electrodynamics quantum optics non-Hermitian quantum physics |
| url | https://www.mdpi.com/2073-8994/14/9/1816 |
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