A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes
Recently, Bennett et al. (Eur. J. Phys. <b>37</b>:014001, 2016) presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spaceti...
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MDPI AG
2019-08-01
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| Online Access: | https://www.mdpi.com/1099-4300/21/9/844 |
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| author | Ben Maybee Daniel Hodgson Almut Beige Robert Purdy |
| author_facet | Ben Maybee Daniel Hodgson Almut Beige Robert Purdy |
| author_sort | Ben Maybee |
| collection | DOAJ |
| description | Recently, Bennett et al. (Eur. J. Phys. <b>37</b>:014001, 2016) presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </semantics> </math> </inline-formula>, and the electric and magnetic field observables, <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi mathvariant="bold">E</mi> <mo stretchy="false">^</mo> </mover> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi mathvariant="bold">B</mi> <mo stretchy="false">^</mo> </mover> </semantics> </math> </inline-formula>, respectively, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect. |
| first_indexed | 2024-04-11T12:31:22Z |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:31:22Z |
| publishDate | 2019-08-01 |
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| spelling | doaj.art-8a9dac8f50cd4689bb5022d258651f942022-12-22T04:23:45ZengMDPI AGEntropy1099-43002019-08-0121984410.3390/e21090844e21090844A Physically-Motivated Quantisation of the Electromagnetic Field on Curved SpacetimesBen Maybee0Daniel Hodgson1Almut Beige2Robert Purdy3Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, 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, UKRecently, Bennett et al. (Eur. J. Phys. <b>37</b>:014001, 2016) presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </semantics> </math> </inline-formula>, and the electric and magnetic field observables, <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi mathvariant="bold">E</mi> <mo stretchy="false">^</mo> </mover> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi mathvariant="bold">B</mi> <mo stretchy="false">^</mo> </mover> </semantics> </math> </inline-formula>, respectively, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect.https://www.mdpi.com/1099-4300/21/9/844quantum electrodynamicsrelativistic quantum information |
| spellingShingle | Ben Maybee Daniel Hodgson Almut Beige Robert Purdy A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes Entropy quantum electrodynamics relativistic quantum information |
| title | A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes |
| title_full | A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes |
| title_fullStr | A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes |
| title_full_unstemmed | A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes |
| title_short | A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes |
| title_sort | physically motivated quantisation of the electromagnetic field on curved spacetimes |
| topic | quantum electrodynamics relativistic quantum information |
| url | https://www.mdpi.com/1099-4300/21/9/844 |
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